Categorial properties of compressed zero-divisor graphs of finite commutative rings

Abstract

We define a compressed zero-divisor graph $\Theta (K)$ of a finite commutative unital ring $K$, where the compression is performed by means of the associatedness relation. We prove that this is the best possible compression which induces a functor $\Theta$, and that this functor preserves categorial products (in both directions). We use the structure of $\Theta (K)$ to characterize important classes of finite commutative unital rings, such as local rings and principal ideal rings.

14 pages

References in corpus (1)

• The total zero-divisor graph of commutative rings

Cited by in corpus (1)

• Compressed zero-divisor graphs of noncommutative rings