Characterizing Topologically Dense Injective Acts and Their Monoid Connections

IF 1.3 4区 数学 Q1 MATHEMATICS Journal of Mathematics Pub Date : 2024-05-27 DOI:10.1155/2024/2966461
Masoomeh Hezarjaribi Dastaki, Hamid Rasouli, Hasan Barzegar
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Abstract

In this paper, we explore the concept of topologically dense injectivity of monoid acts. It is shown that topologically dense injective acts constitute a class strictly larger than the class of ordinary injective ones. We determine a number of acts satisfying topologically dense injectivity. Specifically, any strongly divisible as well as strongly torsion free -act over a monoid is topologically dense injective if and only if is a left reversible monoid. Furthermore, we establish a counterpart of the Skornjakov criterion and also identify a class of acts satisfying the Baer criterion for topologically dense injectivity. Lastly, some homological classifications for monoids by means of this type of injectivity of monoid acts are also provided.
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拓扑密集注入行为的特征及其单体连接
本文探讨了单元行为的拓扑致密可注入性概念。研究表明,拓扑致密注入行为构成了一个严格大于普通注入行为的类别。我们确定了一些满足拓扑密集注入性的行为。具体地说,当且仅当一个左可逆单元上的强可分和强无扭行为是拓扑致密注入行为时,该单元上的任何强可分和强无扭行为都是拓扑致密注入行为。此外,我们还建立了斯科恩贾科夫准则的对应准则,并确定了一类满足贝尔准则的拓扑致密注入性行为。最后,我们还通过这类单形行为的注入性为单形提供了一些同构分类。
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来源期刊
Journal of Mathematics
Journal of Mathematics Mathematics-General Mathematics
CiteScore
2.50
自引率
14.30%
发文量
0
期刊介绍: Journal of Mathematics is a broad scope journal that publishes original research articles as well as review articles on all aspects of both pure and applied mathematics. As well as original research, Journal of Mathematics also publishes focused review articles that assess the state of the art, and identify upcoming challenges and promising solutions for the community.
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