Ascending chain conditions on right ideals of semigroups
Group Theory
2023-01-23 v2
Abstract
We call a semigroup right noetherian if it satisfies the ascending chain condition on right ideals, and we say that satisfies ACCPR if it satisfies the ascending chain condition on principal right ideals. We investigate the behavior of these two conditions with respect to ideals and ideal extensions, with a particular focus on minimal and 0-minimal one-sided ideals. In particular, we show that the property of satisfying ACCPR is inherited by right and left ideals. On the other hand, we exhibit an example of a right noetherian semigroup with a minimal ideal that is not right noetherian.
Cite
@article{arxiv.2209.13607,
title = {Ascending chain conditions on right ideals of semigroups},
author = {Craig Miller},
journal= {arXiv preprint arXiv:2209.13607},
year = {2023}
}