Neutro Ordered Ring

Neutro Ordered Ring

Ahmed Hatip, Necati Olgun
Copyright: © 2022 |Pages: 15
DOI: 10.4018/978-1-6684-3495-6.ch013
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Abstract

The objective of this chapter is to introduce the concept of Neutro Ordered Rings by considering three Neutro Axioms (Neutro Abelian Group [additive], Neutro Semi group [multiplicative], and Neutro Distributive [multiplication over addition]) and total ordered relation or partially ordered relation. The concepts of Neutro Ordered Rings, Neutro Ordered Subrings, Neutro Ordered Ideals, Neutro Ordered Quotient Rings, and Neutro Ordered Ring Homomorphisms are presented. Moreover, several interesting results were reached, and a lot of illustrative examples were added.
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Background

In this section, we will give some background that will be useful in other sections of the research.

Neutrosophic Sets (Smarandache 1998)

Let 978-1-6684-3495-6.ch013.m04 be a universe. A neutrosophic sets 978-1-6684-3495-6.ch013.m05 over 978-1-6684-3495-6.ch013.m06 is defined by

978-1-6684-3495-6.ch013.m07
Where, 978-1-6684-3495-6.ch013.m08, 978-1-6684-3495-6.ch013.m09 and 978-1-6684-3495-6.ch013.m10 are called truth-membership function, indeterminacy-membership function and falsity- membership function, respectively. They are defined by
978-1-6684-3495-6.ch013.m11
Such that 978-1-6684-3495-6.ch013.m12.

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