## Faculty and Staff Publications

#### Document Type

Book

#### Publication Date

2013

#### Abstract

In this book authors bring out how sets in algebraic structure can be used to construct most generalized algebraic structures, like set linear algebra/vector space, set ideals in rings and semigroups. This sort of study is not only innovative but infact very helpful in cases instead of working with a large data we can work with a considerably small data. Thus instead of working with a vector space or a linear algebra V over a field F we can work with a subset in V and a needed subset in F, this can save both time and economy. The concept of quasi set vector subspaces over a set or set vector spaces over a set are some examples of how sets are used and algebraic structures are given to them. Further these set algebraic structures are used in the following, in the first place they are used in the construction of topological spaces of different types, which basically depend on the set over which the collection of subspaces are defined. For instance given a vector space defined over the field we can have one and only one topological space of subspaces associated with it, however for a given vector space we can have several topological set vector spaces associated with it; that too depending on the subsets which we choose in the field F. This notion has several advantages for we can use a needed part of the structure and study the problem.

#### Publisher

Educational Publisher, Ohio

#### ISSN

978-1-59973-212-1

#### Language (ISO)

English

#### Keywords

Algebraic Structures, set theory, neutrosophic logic

#### Recommended Citation

W.B. Vasantha Kandasamy & F. Smarandache. Set Theoretic Approach to Algebraic Structures in Mathematics - A Revelation. Ohio: Educational Publisher Inc, 2013.

#### Creative Commons License

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

#### Included in

Algebra Commons, Algebraic Geometry Commons, Analysis Commons, Discrete Mathematics and Combinatorics Commons, Logic and Foundations Commons, Number Theory Commons