No 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 \textit{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 presimplifiable rings and (hereditarily) strongly associate rings. Further, we consider idealizations, localizations, zero-divisor graphs, and ultraproducts of domainlike rings.