Zero-Divisors of Content Algebras

TL;DR

This paper investigates the behavior of zero-divisors in content algebras, focusing on how minimal primes and zero-divisor graphs are preserved under content extensions, especially over rings with Property (A) or finitely many zero-divisors.

Contribution

It establishes that minimal primes extend to minimal primes in content extensions and analyzes the preservation of zero-divisor graph diameter under these extensions.

Findings

Minimal primes extend to minimal primes in content extensions.

Zero-divisor graph diameter is preserved under content extensions.

Content algebras over rings with Property (A) have structured zero-divisors.

Abstract

In this article, we prove that in content extentions minimal primes extend to minimal primes and discuss zero-divisors of a content algebra over a ring who has Property (A) or whose set of zero-divisors is a finite union of prime ideals. We also examine the preservation of diameter of zero-divisor graph under content extensions.