Discrete mathematics

Physics

Organic chemistry

Pure mathematics

Ideal (ethics)

Ring (chemistry)

Characterization (materials science)

Mathematics

Optics

Epistemology

Maximal ideal

Principal ideal ring

Mathematical analysis

Philosophy

Chemistry

Simple ring

Polynomial

Polynomial ring

HAL (Le Centre pour la Communication Scientifique Directe)

If R(I) is a neutrosophic ring, then every subset of R(I) has the form 𝑀 = 𝑃 + 𝑆𝐼, where P,S are subsets of the classical ring R. The objective of this paper is to determine the necessary and sufficient condition on classical subsets P and S which makes M an ideal in R(I). The main result is proving that every classical ideal in a neutrosophic ring must be an AH-ideal and determining the form of maximal and minimal ideals in R(I). Also, a similar discussion of the case of refined neutrosophic rings will be presented.

On The Characterization Of Maximal and Minimal Ideals In Several Neutrosophic Rings