# Gorenstein-projective and semi-Gorenstein-projective modules. II

## TL;DR

This paper investigates the structure of 3-dimensional local modules over a specific algebra, revealing a family of semi-Gorenstein-projective modules that are not torsionless, expanding understanding of module properties in algebra.

## Contribution

It provides a detailed classification of 3-dimensional local modules over algebra A(q), highlighting new semi-Gorenstein-projective modules not torsionless, especially when q has infinite order.

## Key findings

- Existence of a family of semi-Gorenstein-projective modules not torsionless
- Characterization of modules over algebra A(q) with infinite order q
- Extension of previous results from Part I to a broader class of modules

## Abstract

Let k be a field and q a non-zero element of k. In Part I, we have exhibited a 6-dimensional k-algebra A = A(q) and we have shown that if q has infinite multiplicative order, then A has a 3-dimensional local module which is semi-Gorenstein-projective, but not torsionless, thus not Gorenstein-projective. This Part II is devoted to a detailed study of all the 3-dimensional local A-modules for this particular algebra A. If q has infinite multiplicative order, we will encounter a whole family of 3-dimensional local modules which are semi-Gorenstein-projective, but not torsionless.