Complete Intersection Hom Injective Dimension

TL;DR

This paper introduces a new injective invariant for local rings based on quasi-deformations and Hom functors, which characterizes the complete intersection property and refines existing homological dimensions.

Contribution

It proposes a novel injective complete intersection dimension using Hom functors, expanding the understanding of ring properties and module invariants.

Findings

Characterizes the complete intersection property for local rings

Bounds Bass numbers polynomially for certain modules

Enhances Bass' conjecture for modules of finite injective dimension

Abstract

We introduce and investigate a new injective version of the complete intersection dimension of Avramov, Gasharov, and Peeva. It is like the complete intersection injective dimension of Sahandi, Sharif, and Yassemi in that it is built using quasi-deformations. Ours is different, however, in that we use a Hom functor in place of a tensor product. We show that (a) this invariant characterizes the complete intersection property for local rings, (b) it fits between the classical injective dimension and the G-injective dimension of Enochs and Jenda, (c) it provides modules with Bass numbers that are bounded by polynomials, and (d) it improves a theorem of Peskine, Szpiro, and Roberts (Bass' conjecture).% for finitely generated modules of finite injective dimension.