The ideals of the monoid of all full transformations with restricted range

IF 0.5 3区数学 Q3 MATHEMATICS

Journal of Algebra and Its Applications Pub Date : 2023-10-28 DOI:10.1142/s0219498825500811

Ping Zhao, Huabi Hu

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引用次数: 0

Abstract

Let [Formula: see text] be a non-empty set and let [Formula: see text] be the monoid of all full transformations of [Formula: see text]. Given a non-empty subset [Formula: see text] of [Formula: see text], we denote by [Formula: see text] the subsemigroup of [Formula: see text] of all full transformations with range contained in [Formula: see text] and by [Formula: see text] the monoid of all full transformations of [Formula: see text]. In 2011, Sanwong investigated the subsemigroup [Formula: see text] of [Formula: see text]. For [Formula: see text] is a finite set with [Formula: see text], put [Formula: see text] We characterize the connections between the maximal regular subsemigroups of ideals of [Formula: see text] and the maximal regular subsemigroups of ideals of [Formula: see text]. Moreover, we determine the maximal subsemigroups of [Formula: see text] and classify completely the maximal regular subsemigroups of the ideals [Formula: see text] of [Formula: see text], for [Formula: see text]. We also show that, for [Formula: see text], any maximal regular subsemigroup of [Formula: see text] is idempotent generated.

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具有有限范围的所有满变换的幺一元的理想

设[公式:见文]是一个非空集合，设[公式:见文]是[公式:见文]的所有完整变换的幺一元。给定[公式:见文]的一个非空子集[公式:见文]，我们用[公式:见文]表示范围包含在[公式:见文]中的所有满变换[公式:见文]的子半群[公式:见文]，用[公式:见文]表示[公式:见文]的所有满变换的幺一元。2011年，Sanwong研究了[公式:见文]的子半群[公式:见文]。对于[公式:见文]是具有[公式:见文]的有限集合，我们刻画了[公式:见文]的理想的极大正则子半群与[公式:见文]的理想的极大正则子半群之间的联系。此外，我们确定了[公式:见文]的极大子半群，并对[公式:见文]的理想[公式:见文]的极大正则子半群进行了完全分类。我们还证明，对于[公式:见文]，[公式:见文]的任何极大正则子半群都是幂等生成的。

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来源期刊

Journal of Algebra and Its Applications 数学-数学

CiteScore

1.50

自引率

12.50%

发文量

226

审稿时长

4-8 weeks

期刊介绍： The Journal of Algebra and Its Applications will publish papers both on theoretical and on applied aspects of Algebra. There is special interest in papers that point out innovative links between areas of Algebra and fields of application. As the field of Algebra continues to experience tremendous growth and diversification, we intend to provide the mathematical community with a central source for information on both the theoretical and the applied aspects of the discipline. While the journal will be primarily devoted to the publication of original research, extraordinary expository articles that encourage communication between algebraists and experts on areas of application as well as those presenting the state of the art on a given algebraic sub-discipline will be considered.