On Steinitz-like properties in amalgamated algebras along an ideal

Abstract

Let [Formula: see text] be a ring homomorphism, [Formula: see text] be an ideal of [Formula: see text] and [Formula: see text] the amalgamation of [Formula: see text] with [Formula: see text] along [Formula: see text] with respect to [Formula: see text]. In this paper, we provide necessary and sufficient conditions for [Formula: see text] to be a Steinitz ring, semi-Steinitz ring, and weakly semi-Steinitz. Then we construct new original examples of weakly semi-Steinitz rings which are not semi-Steinitz rings and semi-Steinitz rings which are not Steinitz rings.