Amalgamated algebra extensions defined by Von Neumann regular and SFT conditions

TL;DR

This paper characterizes when amalgamated algebra extensions, defined via a ring homomorphism and an ideal, are Von Neumann regular or SFT rings, providing conditions for these properties.

Contribution

It offers new characterizations of amalgamated algebra extensions that are Von Neumann regular or SFT rings based on the properties of the base ring and ideal.

Findings

Provides necessary and sufficient conditions for amalgamated extensions to be Von Neumann regular.

Provides necessary and sufficient conditions for amalgamated extensions to be SFT rings.

Enhances understanding of algebraic properties of amalgamated algebra constructions.

Abstract

Let $f:A\rightarrow B$ be a ring homomorphism and let $J$ be an ideal of $B$. In this paper, we characterize $R\bowtie^fJ$ to be Von Neumann regular ring and SFT ring, respectively.