Injective generation for graded rings
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866909567782223872 |
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| author | Kostas, Panagiotis Psaroudakis, Chrysostomos |
| author_facet | Kostas, Panagiotis Psaroudakis, Chrysostomos |
| contents | In this paper we investigate injective generation for graded rings. We first examine the relation between injective generation and graded injective generation for graded rings. We then reduce the study of injective generation for graded rings to the study of injective generation for certain Morita context rings and we provide sufficient conditions for injective generation of the latter. We then provide necessary and sufficient conditions so that injectives generate for tensor rings and for trivial extension rings. We provide two proofs for the class of tensor rings, the one uses covering theory and the other uses the framework of cleft extensions of module categories. We finally prove injective generation for twisted tensor products of finite dimensional algebras. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_19574 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Injective generation for graded rings Kostas, Panagiotis Psaroudakis, Chrysostomos Representation Theory Category Theory Rings and Algebras 16E, 16E10, 16E30, 16E35, 16W50, 18G80 In this paper we investigate injective generation for graded rings. We first examine the relation between injective generation and graded injective generation for graded rings. We then reduce the study of injective generation for graded rings to the study of injective generation for certain Morita context rings and we provide sufficient conditions for injective generation of the latter. We then provide necessary and sufficient conditions so that injectives generate for tensor rings and for trivial extension rings. We provide two proofs for the class of tensor rings, the one uses covering theory and the other uses the framework of cleft extensions of module categories. We finally prove injective generation for twisted tensor products of finite dimensional algebras. |
| title | Injective generation for graded rings |
| topic | Representation Theory Category Theory Rings and Algebras 16E, 16E10, 16E30, 16E35, 16W50, 18G80 |
| url | https://arxiv.org/abs/2407.19574 |