## Branch Mathematics and Statistics Faculty and Staff Publications

#### Title

#### Document Type

Book

#### Publication Date

2013

#### Abstract

In this book authors introduce the new notion of constructing non associative algebraic structures using subsets of a groupoid. Thus subset groupoids are constructed using groupoids or loops. Even if we use subsets of loops still the algebraic structure we get with it is only a groupoid. However we can get a proper subset of it to be a subset loop which will be isomorphic with the loop which was used in the construction of the subset groupoid. To the best of the authors’ knowledge this is the first time non associative algebraic structures are constructed using subsets. We get a large class of finite subset groupoids as well as a large class of infinite subset groupoids. Here we find the conditions under which these subset groupoids satisfy special identities like Bol identity, Moufang identity, right alternative identity and so on. In fact it is a open problem to find subset groupoids to satisfy special identities even if the groupoids over which they are defined do not satisfy any of the special identities.

#### Publisher

Educational Publisher Inc., Ohio

#### ISSN

978-1-59973-222-0

#### Language (ISO)

English

#### Keywords

groupoid, Bol identity, Moufang identity, neutrosophic logic

#### Recommended Citation

W.B. Vasantha Kandasamy & F. Smarandache. Subset Groupoids. Ohio: Educational Publisher Inc., 2013.

#### Creative Commons License

This work is licensed under a Creative Commons Attribution-Share Alike 4.0 International License.

#### Included in

Algebra Commons, Algebraic Geometry Commons, Analysis Commons, Logic and Foundations Commons, Number Theory Commons, Other Mathematics Commons, Set Theory Commons