Weakly α-prime ideals

Najib Mahdou

doi:10.1142/S1793557125501232

Weakly α-prime ideals

2025-10-01

0

PRE

AI

DOI：10.1142/S1793557125501232

原文链接

原文求助

摘要

En 中文

In this paper, we introduce and study the notion of weakly alpha-prime ideals. Let R be a commutative ring, I an ideal of R and alpha is an element of End(R). We say that I is a weakly alpha-prime ideal if whenever 0 not equal ab is an element of I, then a is an element of I or alpha(b) is an element of I, equivalently b is an element of I or alpha(a) is an element of I. We show that if I-2 not equal 0, then the notion of alpha-prime and weakly alpha-prime ideals coincide. We give several basic properties of the notion of weakly alpha-prime ideals and we study its transfer to trivial ring extensions and amalgamations of rings. This allows us to construct nontrivial examples of weakly alpha-prime ideals that are neither alpha-prime nor weakly prime ideals.

Keyword:

Weakly alpha-prime ideal

alpha-prime ideal

trivial ring extension

amalgamation of ring along an ideal

Weakly α-prime ideals

摘要

期刊

机构

引用论文