The Zero-Divisor Graph Problem

Research output: Other contribution

Abstract

Abstract: Let $S$ be a commutative semigroup with $0$ element. A nonzero element $a\in S$ is called a zero-divisor if there exists a nonzero element $b\in S$ so that $ab=0$. The zero-divisor graph, $\Gamma (S)$ is the simple graph whose vertices are given by the nonzero zero-divisors of $S$ where two distinct vertices, $a$ and $b$, are adjacent in case $ab=0$ in $S$. We will begin with a discussion of the history of this construction and foundational results, including examples. We conclude with some very recent results, other zero divisor graph constructions, and some open questions.
Original languageEnglish
StatePublished - Nov 2019

Fingerprint

Dive into the research topics of 'The Zero-Divisor Graph Problem'. Together they form a unique fingerprint.

Cite this