Amalgamated Algebras Which Are Présimplifiable or Domainlike

Abstract

A commutative ring $A$ is called présimplifiable (resp., domain-like) if all its zero divsors are contained in its Jacobson radical (resp., $0$ is a primary ideal of $A$). Let $A$ and $B$ be two commutative rings with identity, $J$ be an ideal of $B$, and $\rho: A\rightarrow B$ be a ring homomorphism. In this paper, we give a characterization for the amalgamation of $A$ with $B$ along $J$ with respect to $\rho$ (denoted by $R\Join ^\rho J$) to be présimplifiable (resp., domain-like).