On nonnil-zero-divisor rings

Visweswaran, S.; Patel, H. D.

doi:10.22124/jart.2025.28466.1715

On nonnil-zero-divisor rings

Articles in Press

Document Type : Research Paper

Authors

S. Visweswaran ¹
H. D. Patel ²

¹ Department of Mathematics, Saurashtra University, Rajkot, India

² Science and Humanities Department, Government Polytechnic, Bhuj, India

10.22124/jart.2025.28466.1715

Abstract

The rings considered in this paper are commutative with identity and are nonzero. Let R be a ring. An ideal I of R is said to be nonnil if I is not contained in the nilradical of R. We say that R is a nonnil-zero-divisor ring if for any proper nonnil ideal I of R, the set of zero-divisors of the R-module R/I is a finite union of prime ideals of R. This paper aims to discuss some basic properties of nonnil-zero-divisor rings and to compare the ring-theoretic properties of zero-divisor rings with that of the ring-theoretic properties of nonnil-zero-divisor rings.

Keywords