Modules With Descending Chain Conditions on Endoimages
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866915557712855040 |
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| author | Gera, Theophilus Patel, Manoj Kumar Gupta, Ashok Ji |
| author_facet | Gera, Theophilus Patel, Manoj Kumar Gupta, Ashok Ji |
| contents | We investigate endoartinian modules, which satisfy the descending chain condition on endoimages, and establish new characterizations that unify classical and generalized chain conditions. Over commutative rings, endoartinianity coincides with rings satisfying the strongly ACCR* with dim(R) = 0 and strongly DCCR* conditions. For principally injective rings, the endoartinian and endonoetherian rings are equivalent. Addressing a question of Facchini and Nazemian, we provide a condition under which isoartinian and Noetherian rings coincide, and we classify semiprime endoartinian rings as finite products of matrix rings over a division ring. We further show that endoartinianity is equivalent to the Kothe rings over principal ideal rings with central idempotents, and characterize such rings as finite products of artinian uniserial rings. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2510_14477 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Modules With Descending Chain Conditions on Endoimages Gera, Theophilus Patel, Manoj Kumar Gupta, Ashok Ji Rings and Algebras 16P20, 16P60 (Primary), 13E10 (Secondary) We investigate endoartinian modules, which satisfy the descending chain condition on endoimages, and establish new characterizations that unify classical and generalized chain conditions. Over commutative rings, endoartinianity coincides with rings satisfying the strongly ACCR* with dim(R) = 0 and strongly DCCR* conditions. For principally injective rings, the endoartinian and endonoetherian rings are equivalent. Addressing a question of Facchini and Nazemian, we provide a condition under which isoartinian and Noetherian rings coincide, and we classify semiprime endoartinian rings as finite products of matrix rings over a division ring. We further show that endoartinianity is equivalent to the Kothe rings over principal ideal rings with central idempotents, and characterize such rings as finite products of artinian uniserial rings. |
| title | Modules With Descending Chain Conditions on Endoimages |
| topic | Rings and Algebras 16P20, 16P60 (Primary), 13E10 (Secondary) |
| url | https://arxiv.org/abs/2510.14477 |