论文标题
沿着正确理想的链条条件
Ascending chain conditions on right ideals of semigroups
论文作者
论文摘要
如果在正确的理想下满足上升的链条条件，我们将称其为Semigroup $ s $ right Noetherian，并且我们说，如果$ s $满足ACCPR，那么它可以满足原理正确理想的上升链条条件。我们研究了这两种条件在理想和理想扩展方面的行为，特别关注最小和0分钟的单方面理想。特别是，我们表明，满足ACCPR的属性是左右理想继承的。另一方面，我们展示了一个右Noetherian半群的示例，其最小的理想是不正确的Noetherian。
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.
