Characterizing Topologically Dense Injective Acts and Their Monoid Connections
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. Specifi...
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| Format: | Article |
| Language: | English |
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Wiley
2024-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2024/2966461 |
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| author | Masoomeh Hezarjaribi Dastaki Hamid Rasouli Hasan Barzegar |
| author_facet | Masoomeh Hezarjaribi Dastaki Hamid Rasouli Hasan Barzegar |
| author_sort | Masoomeh Hezarjaribi Dastaki |
| collection | DOAJ |
| description | 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 S-act over a monoid S is topologically dense injective if and only if S 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. |
| format | Article |
| id | doaj-art-9f3276df0ffa410695fd418efb6a68d9 |
| institution | DOAJ |
| issn | 2314-4785 |
| language | English |
| publishDate | 2024-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-9f3276df0ffa410695fd418efb6a68d92025-08-20T03:18:56ZengWileyJournal of Mathematics2314-47852024-01-01202410.1155/2024/2966461Characterizing Topologically Dense Injective Acts and Their Monoid ConnectionsMasoomeh Hezarjaribi Dastaki0Hamid Rasouli1Hasan Barzegar2Department of MathematicsDepartment of MathematicsDepartment of MathematicsIn 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 S-act over a monoid S is topologically dense injective if and only if S 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.http://dx.doi.org/10.1155/2024/2966461 |
| spellingShingle | Masoomeh Hezarjaribi Dastaki Hamid Rasouli Hasan Barzegar Characterizing Topologically Dense Injective Acts and Their Monoid Connections Journal of Mathematics |
| title | Characterizing Topologically Dense Injective Acts and Their Monoid Connections |
| title_full | Characterizing Topologically Dense Injective Acts and Their Monoid Connections |
| title_fullStr | Characterizing Topologically Dense Injective Acts and Their Monoid Connections |
| title_full_unstemmed | Characterizing Topologically Dense Injective Acts and Their Monoid Connections |
| title_short | Characterizing Topologically Dense Injective Acts and Their Monoid Connections |
| title_sort | characterizing topologically dense injective acts and their monoid connections |
| url | http://dx.doi.org/10.1155/2024/2966461 |
| work_keys_str_mv | AT masoomehhezarjaribidastaki characterizingtopologicallydenseinjectiveactsandtheirmonoidconnections AT hamidrasouli characterizingtopologicallydenseinjectiveactsandtheirmonoidconnections AT hasanbarzegar characterizingtopologicallydenseinjectiveactsandtheirmonoidconnections |