## Mathematics and Statistics Faculty and Staff Publications

#### Document Type

Book

#### Publication Date

2013

#### Abstract

In this book authors introduce the notion of subset polynomial semirings and subset matrix semirings. The study of algebraic structures using subsets were recently carried out by the authors. Here we define the notion of subset row matrices, subset column matrices and subset m × n matrices. Study of this kind is developed in chapter two of this book. If we use subsets of a set X; say P(X), the power set of the set X....

Hence if P(X) is replaced by a group or a semigroup we get the subset matrix to be only a subset matrix semigroup. If the semiring or a ring is used we can give the subset collection only the semiring structure. The collection of subsets from the polynomial ring or a polynomial semiring can have only a semiring structure. Several types of subset polynomial semirings are defined described and developed in chapter three of this book.

#### Publisher

Educational Publisher Inc., Ohio

#### ISSN

978-1-59973-223-7

#### Language (ISO)

English

#### Keywords

subset polynomial semirings, subset matrix semirings, neutrosophic logic

#### Recommended Citation

W.B. Vasantha Kandasamy & F. Smarandache. Subset Polynomial Semirings and Subset Matrix Semirings. 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, Logic and Foundations Commons, Number Theory Commons, Other Mathematics Commons, Set Theory Commons