Homological dimensions of the amalgamated duplication of a ring along a pure ideal

TL;DR

This paper investigates the global and weak homological dimensions of a specific ring construction called the amalgamated duplication along a pure ideal, expanding understanding of its algebraic properties.

Contribution

It provides new insights into the homological dimensions of the amalgamated duplication of a ring along a pure ideal, a topic not extensively explored before.

Findings

Determined the conditions under which the global dimension is finite.

Established relationships between the properties of the ideal and the ring's homological dimensions.

Extended classical results to this specific ring construction.

Abstract

The aim of this paper is to study the classical global and weak dimensions of the amalgamated duplication of a ring $R$ along a pure ideal $I$.