English

The ascending chain condition on principal right ideals for semigroup constructions

Group Theory 2023-07-07 v2

Abstract

We call a semigroup R\mathcal{R}-noetherian if it satisfies the ascending chain condition on principal right ideals, or, equivalently, the ascending chain condition on R\mathcal{R}-classes. We investigate the behaviour of the property of being R\mathcal{R}-noetherian under the following standard semigroup-theoretic constructions: semidirect products, Sch\"utzenberger products, free products, Rees matrix semigroups, Brandt extensions, Bruck-Reilly extensions and semilattices of semigroups.

Cite

@article{arxiv.2302.01847,
  title  = {The ascending chain condition on principal right ideals for semigroup constructions},
  author = {Craig Miller},
  journal= {arXiv preprint arXiv:2302.01847},
  year   = {2023}
}
R2 v1 2026-06-28T08:31:31.381Z