Trivial ring extensions and amalgamations of periodic rings

Abstract

In this paper, we investigate the transfer of the notion of periodic ring to trivial ring extensions of commutative ring by modules and amalgamation of rings. Namely, we prove that the trivial ring extension A ∝ E is a periodic ring if and only if so is A. It is also shown that the amalgamation A ⋈^f J is a periodic ring if and only if so is A and J satisfies the periodic-like property.