Title

Properties of domainlike rings

Department/School

Mathematics

Date

6-30-2009

Document Type

Article

Keywords

rings, properties, domainlike rings, R

Abstract

In this paper we will examine properties of and relationships between rings that share some properties with integral domains, but whose definitions are less restrictive. If R is a commutative ring with identity, we call R a domainlike ring if all zero-divisors of R are nilpotent, which is equivalent to (0) being primary. We exhibit properties of domainlike rings, and we compare them to présimplifiable rings and (hereditarily) strongly associate rings. Further, we consider idealizations, localizations, zero-divisor graphs, and ultraproducts of domainlike rings.

Published in

Tamkang Journal of Mathematics

Citation/Other Information

Axtell, M., Forman, S., & Stickles, J. (2009). Properties of domainlike rings. Tamkang Journal of Mathematics, 40(2), 151-164. 10.5556/j.tkjm.40.2009.464.

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