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arXiv · 2209.13607

Ascending chain conditions on right ideals of semigroups

Craig Miller
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Abstract

We call a semigroup $S$ right noetherian if it satisfies the ascending chain condition on right ideals, and we say that $S$ 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.

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Craig Miller. 2022-09-27. Ascending chain conditions on right ideals of semigroups. https://arxiv.org/abs/2209.13607

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