Neutrosophic Set Approach to Algebraic Structures

By Khan, Madad

Book Id: WPLBN0100302943
Format Type: PDF eBook:
File Size: 1.50 MB
Reproduction Date: 10/1/2016

Title:	Neutrosophic Set Approach to Algebraic Structures
Author:	Khan, Madad
Volume:
Language:	English
Subject:	Non Fiction, Science
Collections:	Authors Community, Mathematics
Historic Publication Date:	2016
Publisher:	Educational Publisher

Member Page:	Infinite Science
Citation APA MLA Chicago Khan, B. M., & Smarandache, F. (2016). Neutrosophic Set Approach to Algebraic Structures. Retrieved from http://www.gutenberg.us/

Description
This book consists of seven chapters. In chapter one we introduced neutrosophic ideals (bi, quasi, interior, (m,n) ideals) and discussed the properties of these ideals. Moreover, we characterized regular and intra-regular AG-groupoids using these ideals. In chapter two we introduced neutrosophic minimal ideals in AG-groupoids and discussed several properties. In chapter three, we introduced different neutrosophic regularities of AG-groupoids. Further we discussed several condition where these classes are equivalent. In chapter four, we introduced neutrosophic M-systems and neutrosophic p-systems in non-associative algebraic structure and discussed their relations with neutrosophic ideals. In chapter five, we introduced neutrosophic strongly regular AG-groupoids and characterized this structure using neutrosophic ideals. In chapter six, we introduced the concept of neutrosophic ideal, neutrosophic prime ideal, neutrosophic bi-ideal and neutrosophic quasi ideal of a neutrosophic semigroup. With counter example we have shown that the union and product of two neutrosophic quasi-ideals of a neutrosophic semigroup need not be a neutrosophic quasi-ideal of neutrosophic semigroup. We have also shown that every neutrosophic bi-ideal of a neutrosophic semigroup need not be a neutrosophic quasi-ideal of a neutrosophic semigroup. We have also characterized the regularity and intra-regularity of a neutrosophic semigroup. In chapter seven, we introduced neutrosophic left almost rings and discussed several properties using their neutrosophic ideals.