Some homological properties of an amalgamated duplication of a ring along an ideal

TL;DR

This paper explores how certain homological properties of a ring are preserved or transferred to its amalgamated duplication along an ideal, leading to the creation of new rings with these properties.

Contribution

It introduces new families of rings with specific homological properties by analyzing the transfer from original rings to their amalgamated duplications.

Findings

Identification of conditions for property transfer

Construction of new rings with desired properties

Extension of homological property understanding

Abstract

In this work, we investigate the transfer of some homological properties from a ring $R$ to his amalgamated duplication along some ideal $I$ of $R$, and then generate new and original families of rings with these properties.