Algebra

1607 Submissions

[64] viXra:1607.0508 [pdf] submitted on 2016-07-27 01:56:49

On Neutrosophic Quadruple Algebraic Structures

Authors: S.A. Akinleye, F. Smarandache, A.A.A. Agboola
Comments: 5 Pages.

In this paper we present the concept of neutrosophic quadruple algebraic structures. Specially, we study neutrosophic quadruple rings and we present their elementary properties.
Category: Algebra

[63] viXra:1607.0499 [pdf] submitted on 2016-07-27 03:00:47

Affirmative Resolve of Kothe Conjecture

Authors: T.Nakashima
Comments: 1 Page.

Affirmative resolve of Kothe conjecture
Category: Algebra

[62] viXra:1607.0498 [pdf] submitted on 2016-07-27 03:02:03

The Counter Example of Jacobson Conjecture

Authors: T.Nakashima
Comments: 1 Page.

The counter example of Jacobson conjecture
Category: Algebra

[61] viXra:1607.0350 [pdf] submitted on 2016-07-18 07:16:53

Multi-Structure and Multi-Space

Authors: Florentin Smarandache
Comments: 3 Pages.

I consider that life and practice do not deal with pure spaces, but with a group of many spaces, with a mixture of structures, a 'mongrel', a heterogeneity - the ardently preoccupation is to reunite them! to constitute a multi-structure.
Category: Algebra

[60] viXra:1607.0345 [pdf] submitted on 2016-07-18 07:22:25

Notes On Using T.I.-82 Calculators To Find Sums

Authors: Florentin Smarandache
Comments: 4 Pages.

A sequence is the range of a function whose domain is a subset of Z.
Category: Algebra

[59] viXra:1607.0340 [pdf] submitted on 2016-07-18 07:28:27

On an Erdös’ Open Problems

Authors: Florentin Smarandache
Comments: 3 Pages.

In one of his books (“Analysis…”) Mr. Paul Erdös proposed the following problem.
Category: Algebra

[58] viXra:1607.0339 [pdf] submitted on 2016-07-18 07:29:13

On Another Erdös’ Open Problem

Authors: Florentin Smarandache
Comments: 2 Pages.

Paul Erdös has proposed the following problem.
Category: Algebra

[57] viXra:1607.0337 [pdf] submitted on 2016-07-18 07:31:31

On Carmichaël’s Conjecture

Authors: Florentin Smarandache
Comments: 4 Pages.

In this article we prove that the equation ϕ (x) = n admits a finite number of solutions, we find the general form of these solutions
Category: Algebra

[56] viXra:1607.0336 [pdf] submitted on 2016-07-18 07:32:21

On A Diophantine Equation

Authors: Florentin Smarandache
Comments: 3 Pages.

In this note we present a method of solving this Diophantine equation, method which is different from Ljunggren’s, Mordell’s, and R.K.Guy’s.
Category: Algebra

[55] viXra:1607.0335 [pdf] submitted on 2016-07-18 07:33:54

One Application of Wallis Theorem

Authors: Bencze MihÁly, Florentin Smarandache
Comments: 4 Pages.

By multiplication we obtain the statement. We prove in the same way for cos x.
Category: Algebra

[54] viXra:1607.0332 [pdf] submitted on 2016-07-18 07:37:01

Où se Trouve la Faute ? (Equations Diophantiennes)

Authors: Florentin Smarandache
Comments: 3 Pages.

Où se trouve la faute ? (equations diophantiennes).
Category: Algebra

[53] viXra:1607.0328 [pdf] submitted on 2016-07-18 07:49:06

P-Q Relationships and Sequences

Authors: Florentin Smarandache
Comments: 3 Pages.

This article is on P-Q Relationships and Sequences.
Category: Algebra

[52] viXra:1607.0327 [pdf] submitted on 2016-07-18 07:50:34

Prime Conjecture

Authors: Florentin Smarandache
Comments: 3 Pages.

Any odd number can be expressed as a sum of two primes.
Category: Algebra

[51] viXra:1607.0326 [pdf] submitted on 2016-07-18 07:51:57

Quelques Propriétés Des Medianes

Authors: Florentin Smarandache
Comments: 2 Pages.

Cet article généralise cerrtains résultats sur les nédiannes.
Category: Algebra

[50] viXra:1607.0321 [pdf] submitted on 2016-07-18 07:57:53

Sequences of Sub-Sequences

Authors: Florentin Smarandache
Comments: 4 Pages.

This article is on Sequences of Sub-Sequences.
Category: Algebra

[49] viXra:1607.0320 [pdf] submitted on 2016-07-18 07:59:18

C. Dumirescu, N. VÎRLAN, ȘT. Zamfir, e. RĂDESCU, N. RĂDESCU, Florentin Smarandache

Authors: Smarandache Type Function Obtained by Duality
Comments: 17 Pages.

In this paper we extended the Smarandache function from the set N' of positive integers to the set Q of rationals.
Category: Algebra

[48] viXra:1607.0318 [pdf] submitted on 2016-07-18 08:00:58

Solving Problems by Using a Function in The Number Theory

Authors: Florentin Smarandache
Comments: 4 Pages.

liVe have constructed a function n which associates to each non-null integer m the smallest positive n such that n! is a multiple of m.
Category: Algebra

[47] viXra:1607.0317 [pdf] submitted on 2016-07-18 08:01:42

Some Periodical Sequences

Authors: Florentin Smarandache
Comments: 4 Pages.

Let N be a positive integer with not all digits the same, and N' its digital reverse.
Category: Algebra

[46] viXra:1607.0312 [pdf] submitted on 2016-07-18 08:06:10

Subjective Questions and Anwers for A Math Instructor of Higher Education

Authors: Florentin Smarandache
Comments: 16 Pages.

What are the instructor's general responsabilities ?
Category: Algebra

[45] viXra:1607.0311 [pdf] submitted on 2016-07-18 08:07:19

Sur la Resolution Dans L’ensemble Des Naturels Des Equationes Linéaires

Authors: Florentin Smarandache
Comments: 4 Pages.

L'utilité du cet article est qu'il établit si le nombre des solutions naturelles d'une équation linéaire est limité ou non.
Category: Algebra

[44] viXra:1607.0310 [pdf] submitted on 2016-07-18 08:08:59

Sur la Resolution D’équations du Second Degré a Deux Inconnues Dans Z

Authors: Florentin Smarandache
Comments: 3 Pages.

Cet article nous presente la resolution l’équations du second degré a deux inconnues dans Z.
Category: Algebra

[43] viXra:1607.0309 [pdf] submitted on 2016-07-18 08:10:57

Sur Quelques Progressions

Authors: Florentin Smarandache
Comments: 3 Pages.

Dans cet article on construit des ensembles qui ont la proprieté suivente: quel que soit leur partage en (Leux sous-ensembles, au moins l'un de ces sous-ensembles contient au moins trois éléments en progression arithmétique (ou bien géométrique).
Category: Algebra

[42] viXra:1607.0308 [pdf] submitted on 2016-07-18 08:11:45

The A.m.a.t.y.c. Competition

Authors: Florentin Smarandache
Comments: 3 Pages.

The American Mathematical Association of Two-Year Colleges organizes each year a mathematical competition.
Category: Algebra

[41] viXra:1607.0299 [pdf] submitted on 2016-07-18 08:28:30

Une Application de la Generalisation du Théorème du Ceva

Authors: Florentin Smarandache
Comments: 4 Pages.

Cet article presente une application de la generalisation du théorème du Ceva.
Category: Algebra

[40] viXra:1607.0298 [pdf] submitted on 2016-07-18 08:29:56

Une Classe D’ensembles Recursifs

Authors: Florentin Smarandache
Comments: 8 Pages.

Dans cet article on construit une classe d' ensembles récursifs, on établit des propriétés de ces ensembles et on propose des applications.
Category: Algebra

[39] viXra:1607.0297 [pdf] submitted on 2016-07-18 08:30:57

Une Généralisation de L’inegalité Cauchy Bouniakovski-Schwartz

Authors: Florentin Smarandache
Comments: 2 Pages.

Cet article presente une généralisation de l’inegalité Cauchy-Bouniakovski-Schwartz.
Category: Algebra

[38] viXra:1607.0296 [pdf] submitted on 2016-07-18 08:32:37

Une Generalisation du Theoreme D’Euler

Authors: Florentin Smarandache
Comments: 6 Pages.

Dans les paragraphes qui suivent nous alions démontrer un resultat qui remplace le teorème d' Euler.
Category: Algebra

[37] viXra:1607.0295 [pdf] submitted on 2016-07-18 08:33:58

Une Généralisation de L’inegalité de Hölder

Authors: Florentin Smarandache
Comments: 3 Pages.

On géneralise l'inégalité de Holder grâce à un raisonement par récurrence.
Category: Algebra

[36] viXra:1607.0294 [pdf] submitted on 2016-07-18 08:34:54

Une Généralisation de L’inégalité de Minkowski

Authors: Florentin Smarandache
Comments: 2 Pages.

Cet article presente une généralisation de l’inégalité de Minkowski.
Category: Algebra

[35] viXra:1607.0293 [pdf] submitted on 2016-07-18 08:35:50

Une Généralisation de L’inegalité de Tcebychev

Authors: Florentin Smarandache
Comments: 2 Pages.

Cet article presente une généralisation de l’inegalité de Tcebychev.
Category: Algebra

[34] viXra:1607.0292 [pdf] submitted on 2016-07-18 08:36:49

Une Généralisation D’une Théorème de Carnot

Authors: Florentin Smarandache
Comments: 3 Pages.

Cet article presente une généralisation d’une théorème de Carnot.
Category: Algebra

[33] viXra:1607.0287 [pdf] submitted on 2016-07-18 04:49:33

About Bernoulli's Numbers

Authors: Bencze MihÁly, Florentin Smarandache
Comments: 4 Pages.

Many methods to compute the sum ofthe same powers of the first n natural numbers are well-known. In this paper we present a simple proof of the method.
Category: Algebra

[32] viXra:1607.0285 [pdf] submitted on 2016-07-18 04:52:25

About the Characteristic Function of the Set

Authors: Bencze MihÁly, Florentin Smarandache
Comments: 12 Pages.

In our paper we give a method, based on characteristic function of the set, of resolving some difficult problem of set theory found in high school study.
Category: Algebra

[31] viXra:1607.0284 [pdf] submitted on 2016-07-18 04:55:44

About Very Perfect Numbers

Authors: Bencze MihÁly, Florin Popovici, Florentin Smarandache
Comments: 3 Pages.

the square of an odd prime number can't be very perfect number.
Category: Algebra

[30] viXra:1607.0282 [pdf] submitted on 2016-07-18 04:58:02

A Function in the Number Theory

Authors: Florentin Smarandache
Comments: 7 Pages.

In this paper I shall construct a function n having the following properties.
Category: Algebra

[29] viXra:1607.0277 [pdf] submitted on 2016-07-18 05:10:32

A Generalization of Euler’s Theorem

Authors: Florentin Smarandache
Comments: 7 Pages.

In the paragraphs which follow we will prove a result which replaces the theorem of Euler.
Category: Algebra

[28] viXra:1607.0276 [pdf] submitted on 2016-07-18 05:11:16

A Generalization of the Inequality of Hölder

Authors: Florentin Smarandache
Comments: 3 Pages.

One generalizes the inequality of Hödler thanks to a reasoning by recurrence. As particular cases, one obtains a generalization of the inequality of Cauchy-Buniakovski-Scwartz, and some interesting applications.
Category: Algebra

[27] viXra:1607.0275 [pdf] submitted on 2016-07-18 05:12:13

A Generalization of the Leibniz Theorem

Authors: Bencze MihÁly, Florin Popovici, Florentin Smarandache
Comments: 6 Pages.

In this paper we show a generalization of Leibniz's theorem and an application of this.
Category: Algebra

[26] viXra:1607.0263 [pdf] submitted on 2016-07-18 05:28:21

An Infinity Of Unsolved Problems Concerning A Function In The Number Theory

Authors: Florentin Smarandache
Comments: 23 Pages.

W.Sierpinski has asserted to an international conference that if mankind lasted for ever and numbered the unsolved problems, then in the long run all these unsolved problems would be solved.
Category: Algebra

[25] viXra:1607.0262 [pdf] submitted on 2016-07-18 05:29:13

An Integer Number Algorithm To Solve Linear Equations

Authors: Florentin Smarandache
Comments: 6 Pages.

An algorithm is given that ascertains whether a linear equation has integer number solutions or not; if it does, the general integer solution is determined.
Category: Algebra

[24] viXra:1607.0261 [pdf] submitted on 2016-07-18 05:30:26

Another Integer Algorithm To Solve Linear Equations (Using Congruences)

Authors: Florentin Smarandache
Comments: 8 Pages.

In this section is presented a new integer number algorithm for linear equation.This algorithm is more “rapid” than W. Sierpinski’s presented in the sense that it reaches the general solution after a smaller number of iterations. Its correctness will be thoroughly demonstrated.
Category: Algebra

[23] viXra:1607.0259 [pdf] submitted on 2016-07-18 05:33:51

A Numerical Function in Congruence Theory

Authors: Florentin Smarandache
Comments: 5 Pages.

In this article we define a function L which will allow us to generalize (separately or simultaneously) some theorems from Numbers Theory obtained by Wilson, Fermat, Euler, Gauss, Lagrange, Leibnitz, Moser, Sierpinski.
Category: Algebra

[22] viXra:1607.0255 [pdf] submitted on 2016-07-18 05:37:55

A Property For A Counterexample To Carmichaël’s Conjec

Authors: Florentin Smarandache
Comments: 3 Pages.

There are many papers on this subject, but the author cites the papers which have influenced him, especially Klee’s papers.
Category: Algebra

[21] viXra:1607.0252 [pdf] submitted on 2016-07-18 05:41:53

Asupra Unei Metode a Lui W. Sierpinski de Rezolvare în Numere întregi a Ecuațiilor Liniare

Authors: Florentin Smarandache
Comments: 3 Pages.

In nota urmatoare se fac cateva remarci privind metoda expusa de Sierpinski, remarci ce au ca scop sirnplificarea si extinderea acestei metode.
Category: Algebra

[20] viXra:1607.0251 [pdf] submitted on 2016-07-18 05:43:32

Asupra Unor Conjecturi si Probleme Nerezolvate Referitoare la O Functie in Teoria Numerelor

Authors: Florentin Smarandache
Comments: 15 Pages.

Am construit o functie care asociaza fiecarui intreg nenul n cel mai mic intreg pozitiv m astfel incat m! este multiplu de n.
Category: Algebra

[19] viXra:1607.0247 [pdf] submitted on 2016-07-18 05:58:29

Coefficients K-Nomiaux

Authors: Florentin Smarandache
Comments: 4 Pages.

Dans cet article on élargit les notions de "coefficients binomiaux" et de "coefficients trinomiaux" à la notion de"coefficients k-nomiaux~ et on obtient quelques propriétés générales de ceux-ci. Comme application, on généralisera le "triangle de Pascal".
Category: Algebra

[18] viXra:1607.0246 [pdf] submitted on 2016-07-18 06:00:10

Conjectures On Primes' Summation

Authors: Florentin Smarandache
Comments: 4 Pages.

Any odd integer n can be expressed as a combination of three primes.
Category: Algebra

[17] viXra:1607.0245 [pdf] submitted on 2016-07-18 06:01:23

Conjectures Which Generalize Andrica's Conjecture

Authors: Florentin Smarandache
Comments: 5 Pages.

Five conjectures on paires of consecutive primes are listed below with examples in each case.
Category: Algebra

[16] viXra:1607.0243 [pdf] submitted on 2016-07-18 06:03:33

Contributii la Studiul Unor Functii si Conjecturi in Teoria Numerelor

Authors: Florentin Smarandache
Comments: 28 Pages.

Teoria Numerelor reprezinta pentru mine o pasiune. Rezultatele expuse mai departe constituie rodul catorva ani buni de cercetari si cautari.
Category: Algebra

[15] viXra:1607.0242 [pdf] submitted on 2016-07-18 06:04:48

Convergence D’une Famille de Series in

Authors: Florentin Smarandache
Comments: 4 Pages.

Dans cet article, on construit une famille d'expressions E (n).
Category: Algebra

[14] viXra:1607.0237 [pdf] submitted on 2016-07-18 06:12:59

Des Fantaisies Mathématiques

Authors: Florentin Smarandache
Comments: 2 Pages.

Ces fantaisies mathematiques sont des divertissements, des problèmes amusants : elles font abstraction de la logique communne, mais elles ont quand meme leur "logique", une logique fantaisiste.
Category: Algebra

[13] viXra:1607.0236 [pdf] submitted on 2016-07-18 06:14:14

Digital Subsequences

Authors: Florentin Smarandache
Comments: 4 Pages.

We screen this sequence, selecting only the terms whose digits also satisfy the property or relationship.
Category: Algebra

[12] viXra:1607.0235 [pdf] submitted on 2016-07-18 06:24:48

Enseignement et Recherche Scientifique (Dans Les Mathematiques

Authors: Florentin Smarandache
Comments: 4 Pages.

De nos jours on met un accent puissant sur la correlation de l'enseignement avec la recherche et la production.
Category: Algebra

[11] viXra:1607.0232 [pdf] submitted on 2016-07-18 06:27:47

Functii Aritmetice

Authors: Florentin Smarandache
Comments: 9 Pages.

Este bine cunoscuta importanta functiilor aritmetice in teoria numerelor, importanta datorata pe de-a parte bogatiei rezultatelor ce se obtin cu ajutorul acestor functii, si pe de alta parte frumusetii acestor rezultate.
Category: Algebra

[10] viXra:1607.0231 [pdf] submitted on 2016-07-18 06:28:46

Functii Prime si Coprime

Authors: Florentin Smarandache
Comments: 2 Pages.

Vom construi urmatoare1e functii pe care le numim prime.
Category: Algebra

[9] viXra:1607.0224 [pdf] submitted on 2016-07-18 06:43:25

Happy New Mathematical Years!

Authors: Florentin Smarandache
Comments: 2 Pages.

Due to professor Gane Policarp’s kindness, I have several issues of “Caietul de informare matematică” (“The Notebook of Mathematical Information”), which has beenput together with attention to detail and skill, and which attracted and persuaded me, fromthe very beginning, to collaborate with small materials.
Category: Algebra

[8] viXra:1607.0220 [pdf] submitted on 2016-07-18 06:48:58

Inconsistent Systems of Axioms and Contradictory Theory

Authors: Florentin Smarandache
Comments: 3 Pages.

We construct the system of n+2 axioms.
Category: Algebra

[7] viXra:1607.0219 [pdf] submitted on 2016-07-18 06:49:51

Inequalities for The Integer Part Function In

Authors: Bencze MihÁly, Florin Popovici, Florentin Smarandache
Comments: 4 Pages.

In this paper we prove some inequalities for the integer part function and we give some applications in the number theory.
Category: Algebra

[6] viXra:1607.0218 [pdf] submitted on 2016-07-18 06:51:02

In Legatura cu O Problema de la Concursul de Matematica, Faza Locala, Ramnicu Valcea

Authors: Florentin Smarandache
Comments: 2 Pages.

Se prezinta in aceasta nota o extindere a unei probleme data la Olimpiada de matematica, faza locala, la Ramnicul VaIcea, clasa a VI-a, 1980.
Category: Algebra

[5] viXra:1607.0216 [pdf] submitted on 2016-07-18 06:53:18

Integer Solutions of Linear Equations

Authors: Florentin Smarandache
Comments: 9 Pages.

In this article are presented Definitions and properties of the integer solutions of linear equations.
Category: Algebra

[4] viXra:1607.0212 [pdf] submitted on 2016-07-18 06:58:28

Où se Trouve la Faute Dans ce Raisonnement Par Reccurence?

Authors: Florentin Smarandache
Comments: 2 Pages.

A un concours d'entré en faculté on pose le problème suivant.
Category: Algebra

[3] viXra:1607.0211 [pdf] submitted on 2016-07-18 06:59:23

Où se Trouve la Faute Sur Les Integrales?

Authors: Florentin Smarandache
Comments: 2 Pages.

Où se trouve la faute sur les integrales?
Category: Algebra

[2] viXra:1607.0160 [pdf] submitted on 2016-07-13 11:02:35

General Integration Theory Defined from Extended Cohomology.

Authors: Johan Noldus
Comments: 5 Pages.

We engage in an approach towards integration theory divorced from measure theory concentrating on the dierentiable functions instead of the measurable ones. In a sense, we do for \measure theory" what dierential geometry does for topology; the nal goal of this paper being the rigorous denition of a generalization of the Feynman path integral. The approach taken is an axiomatic one in which it is more important to understand relationships between certain quantities rather than to calculate them exactly. In a sense, this is how the eld of algebraic geometry is developed in opposition to the study of partial dierential equations where in the latter case, the stress is unfortunately still too much on the construction of explicit solutions rather than on structural properties of and between solutions.
Category: Algebra

[1] viXra:1607.0075 [pdf] submitted on 2016-07-06 23:42:10

Schanuel’s Conjecture’s Partial Resolve

Authors: T.Nakashima
Comments: 1 Page.

Schanuel’s conjecture’s partial resolve
Category: Algebra