Quotient Gamma Nearness Rings

Abstract

The aim of this paper is to defined the quotient gamma nearness rings and to examine its properties. We generalize an important theorem for quotient gamma nearness rings. More clearly, we prove the following theorem: Let M≠0M be a commutative Γ-nearness ring such that Nr(B)∗(Nr(B)∗M)=Nr(B)∗M, P be a Γ-nearness ideal of M such that Nr(B)∗(Nr(B)∗P)=Nr(B)∗P, and ∼Br be a congruence indiscernibility relation on M. Then, P is a prime Γ-nearness ideal if and only if M/P is a Γ-nearness integral domain. © Università degli Studi di Napoli "Federico II" 2024.