Indecomposable Injectives over the Jacobson Algebra
Rings and Algebras
2024-10-10 v1
Abstract
Let K be any field. In this paper we give a complete list of the indecomposable left injective module over the Jacobson algebra K<X,Y | XY = 1>, i.e., the free associative K-algebra on two (noncommuting) generators, modulo the single relation XY = 1. This is the natural continuation of the paper of the second two authors with Gene Abrams on the charaterization of the injective envelope of the simple modules over K<X, Y | XY = 1>.
Cite
@article{arxiv.2410.05790,
title = {Indecomposable Injectives over the Jacobson Algebra},
author = {Riccardo Colpi and Francesca Mantese and Alberto Tonolo},
journal= {arXiv preprint arXiv:2410.05790},
year = {2024}
}