# Algebra

## 1404 Submissions

[2] **viXra:1404.0120 [pdf]**
*submitted on 2014-04-14 11:09:26*

### Algebraic Structures on Fuzzy Unit Square and Neutrosophic Unit Square

**Authors:** W. B. vasantha Kandasamy, Florentin Smarandache

**Comments:** 221 Pages.

In this book authors build algebraic structures on fuzzy unit semi-open square UF = {(a,b), with a, b in [0, 1)} and on neutrosophic unit semi-open square UN = {a+bI, with a, b in [0, 1)}.
As distributive laws are not true, we are not in a position to develop several properties of rings, semirigs and linear algebras. Seven open conjectures are proposed.

**Category:** Algebra

[1] **viXra:1404.0119 [pdf]**
*submitted on 2014-04-14 11:10:37*

### Groupoids of Type I and II Using [0, n)

**Authors:** W. B. vasantha Kandasamy, Florentin Smarandache

**Comments:** 178 Pages.

Study of algebraic structures built using [0, n) looks to be one of interesting and innovative research. Here we define two types of groupoids using [0, n), both of them are of infinite order. It is an open conjecture to find whether this new class of groupoids satisfy any of the special identities like Moufang identity or Bol identity and so on.

**Category:** Algebra