English

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>.

Keywords

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}
}
R2 v1 2026-06-28T19:12:36.906Z