On graded Gorenstein injective dimension

TL;DR

This paper investigates the properties of the graded Gorenstein injective dimension of complexes of graded modules, establishing formulas and comparisons with the classical Gorenstein injective dimension.

Contribution

It introduces the concept of graded Gorenstein injective dimension, proves a Chouinard-like formula, and compares it with the standard Gorenstein injective dimension.

Findings

Established a Chouinard-like formula for graded Gorenstein injective dimension

Compared graded and ungraded Gorenstein injective dimensions

Derived properties relating graded homological dimensions

Abstract

There are nice relations between graded homological dimensions and ordinary homological dimensions. We study the Gorenstein injective dimension of a complex of graded modules denoted by $^*\Gid$, and derive its properties. In particular we prove the Chouinard's like formula for $^*\Gid$, and compare it with the usual Gorenstein injective dimension.