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| Main Authors: | , |
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| Format: | Preprint |
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2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2509.24292 |
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| _version_ | 1866914075009613824 |
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| author | Madanshekaf, Ali Farsad, Farideh |
| author_facet | Madanshekaf, Ali Farsad, Farideh |
| contents | In this paper, we introduce and explore new classes of S-acts over a monoid S, namely, strongly Hopfian and strongly co-Hopfian acts, as well as their weaker counterparts, Hopfian and co-Hopfian acts. We investigate the relationships between these newly defined structures and well-studied classes of S-acts, including Noetherian, Artinian, injective, projective, quasi-injective, and quasi-projective acts. A key result shows that, under certain conditions, a quasi-projective (respectively quasi-injective) S-act that is strongly co-Hopfian (respectively strongly Hopfian) is also strongly Hopfian (respectively strongly co-Hopfian). Moreover, we provide a variety of examples and structural results concerning the behavior of subacts and quotient acts of strongly Hopfian and strongly co-Hopfian S-acts, further elucidating the internal structure and interrelationships within this extended framework. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_24292 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Strongly Hopfian and Co-Hopfian Acts over Monoids: Structure and Characterizations Madanshekaf, Ali Farsad, Farideh Representation Theory 20M30, 20M50 In this paper, we introduce and explore new classes of S-acts over a monoid S, namely, strongly Hopfian and strongly co-Hopfian acts, as well as their weaker counterparts, Hopfian and co-Hopfian acts. We investigate the relationships between these newly defined structures and well-studied classes of S-acts, including Noetherian, Artinian, injective, projective, quasi-injective, and quasi-projective acts. A key result shows that, under certain conditions, a quasi-projective (respectively quasi-injective) S-act that is strongly co-Hopfian (respectively strongly Hopfian) is also strongly Hopfian (respectively strongly co-Hopfian). Moreover, we provide a variety of examples and structural results concerning the behavior of subacts and quotient acts of strongly Hopfian and strongly co-Hopfian S-acts, further elucidating the internal structure and interrelationships within this extended framework. |
| title | Strongly Hopfian and Co-Hopfian Acts over Monoids: Structure and Characterizations |
| topic | Representation Theory 20M30, 20M50 |
| url | https://arxiv.org/abs/2509.24292 |