Properties of Domainlike Rings

M. Axtell；S. J. Forman；J. Stickles

Tamkang Journal of Mathematics

40卷2期（2009 / 06 / 01）

151 - 164

英文

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.