# Algebra

## 1608 Submissions

[3] **viXra:1608.0308 [pdf]**
*submitted on 2016-08-24 06:17:36*

### DSm Field and Linear Algebra of Refined Labels

**Authors:** Florentin Smarandache, Jean Dezert, Xinde Li

**Comments:** 11 Pages.

This chapter presents the DSm Field and Linear Algebra of Refined Labels (FLARL) in DSmT framework in order to work precisely with qualitative labels for information fusion. We present and justify the basic operators on qualitative labels (addition, subtraction,
multiplication, division, root, power, etc).

**Category:** Algebra

[2] **viXra:1608.0136 [pdf]**
*submitted on 2016-08-12 21:45:01*

### Unit Graph of Some Finite Group Zn, Cn and Dn

**Authors:** A. D. Godase, M. B. Dhakne

**Comments:** 10 Pages.

We represent finite group in the form of a graph, these graphs are called unit graph. Since
the main role in obtaining the graph is played by the unit element of the group, this study is
innovative. Also study of different properties like the subgroups of a group, normal
subgroups of a group are carried out using the unit graph of the group.

**Category:** Algebra

[1] **viXra:1608.0039 [pdf]**
*submitted on 2016-08-03 18:36:06*

### Solving Boolean Equation

**Authors:** Oh Jung Uk

**Comments:** 19 Pages.

If ∀P:proposition, B(P) is the truth value(0 or 1) of P then we can solve a boolean equation by using these below.
B(p_1∨p_2∨…∨p_n )≡1+∏_(k=1)^n▒(1+p_k ) (mod 2)
{ (x_1,x_2,…,x_n ) | ∏_(i=1)^n▒B(x_i ) ≡0(mod 2)}=(⋂_(i=1)^n▒{ (x_i ) | B(x_i )≡1(mod 2)} )^c={(x_1,x_2,…,x_n ) |(1,1,1,…,1)}^c

**Category:** Algebra