# Algebra

## 1507 Submissions

[3] **viXra:1507.0148 [pdf]**
*submitted on 2015-07-19 17:54:56*

### Algebraic Problems and Exercises for High School (Sets, Sets Operations, Relations, Functions, Aspects of Combinatorics)

**Authors:** Ion Goian, Raisa Grigor, Vasile Marin, Florentin Smarandache

**Comments:** 144 Pages. Translation from Romanian to English by Ana Maria Buzoianu

In this book, you will find algebra exercises and problems, grouped by chapters, intended for higher grades in high schools or middle schools of general education. Its purpose is to facilitate training in mathematics for students in all high school categories, but can be equally helpful in a standalone workout. The book can also be used as an extracurricular source, as the reader shall find enclosed important theorems and formulas, standard definitions and notions that are not always included in school textbooks.

**Category:** Algebra

[2] **viXra:1507.0122 [pdf]**
*submitted on 2015-07-16 09:28:54*

### Theory of Abel Grassmann's Groupoids

**Authors:** Madad Khan, Florentin Smarandache, Saima Anis

**Comments:** 208 Pages.

An AG-groupoid is an algebraic structure that lies in between a groupoid
and a commutative semigroup. It has many characteristics similar to that of a
commutative semigroup. If we consider x^2y^2= y^2x^2, which holds for all x, y in a
commutative semigroup, on the other hand one can easily see that it holds in an
AG-groupoid with left identity e and in AG**-groupoids. This simply gives that
how an AG-groupoid has closed connections with commutative algebras.
We extend now for the first time the AG-Groupoid to the Neutrosophic
AG-Groupoid. A neutrosophic AG-groupoid is a neutrosophic algebraic
structure that lies between a neutrosophic groupoid and a neutrosophic
commutative semigroup.

**Category:** Algebra

[1] **viXra:1507.0089 [pdf]**
*submitted on 2015-07-13 11:51:55*

### Irreducible Representations of Small Abstract Groups Computed with GAP

**Authors:** Richard J. Mathar

**Comments:** 102 Pages.

This is a table of all irreducible matrix representations of all 181 groups up to order 40,
generated with the GAP software.

**Category:** Algebra