半群及其双理想的高度

Int. J. Algebra Comput. Pub Date : 2022-11-28 DOI:10.1142/s0218196723500054

Craig Miller

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引用次数: 0

摘要

[公式:见文]-半群[公式:见文]的高度是[公式:见文]-类[公式:见文]的偏序集[公式:见文]的高度，给定一个[公式:见文]-高度有限的半群[公式:见文]，我们在[公式:见文]-双理想、单侧理想和双面理想的高度上建立界;特别地，这些子结构继承了高度有限的特性[公式:见文本]。然后我们研究这些界限是否可以达到。

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The ℛ-height of semigroups and their bi-ideals

The [Formula: see text]-height of a semigroup [Formula: see text] is the height of the poset of [Formula: see text]-classes of [Formula: see text] Given a semigroup [Formula: see text] with finite [Formula: see text]-height, we establish bounds on the [Formula: see text]-height of bi-ideals, one-sided ideals and two-sided ideals; in particular, these substructures inherit the property of having finite [Formula: see text]-height. We then investigate whether these bounds can be attained.

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Int. J. Algebra Comput.

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