论文标题
$ \ Mathcal {r} $ - 半群的高度及其双层
The $\mathcal{R}$-height of semigroups and their bi-ideals
论文作者
论文摘要
$ \ MATHCAL {R} $ - 半群$ s $的高度是$ \ Mathcal {r} $ - $ s的poset的高度，$ s，$ s，$ s，$ s，$ s，$ \ MATHCAL {r} $ - 类的链长的上限。给定有有限$ \ MATHCAL {r} $ - 高度的Semigroup $ S $，我们在$ \ Mathcal {r} $ - 双层，单方面的理想和双面理想的高度上建立了界限；特别是，这些子结构继承了具有有限$ \ mathcal {r} $ - 高度的属性。然后，我们研究是否可以达到这些界限。
The $\mathcal{R}$-height of a semigroup $S$ is the height of the poset of $\mathcal{R}$-classes of $S,$ i.e. the supremum of the lengths of chains of $\mathcal{R}$-classes. Given a semigroup $S$ with finite $\mathcal{R}$-height, we establish bounds on the $\mathcal{R}$-height of bi-ideals, one-sided ideals and two-sided ideals; in particular, these substructures inherit the property of having finite $\mathcal{R}$-height. We then investigate whether these bounds can be attained.
