Correct classes of modules
Vernadsky National Library of Ukraine
Переглянути архів Інформація| Поле | Співвідношення | |
| Title |
Correct classes of modules
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| Creator |
Wisbauer, R.
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| Description |
For a ring R, call a class C of R-modules (pure-) mono-correct if for any M, N ∈ C the existence of (pure) monomorphisms M → N and N → M implies M ≃ N. Extending results and ideas of Rososhek from rings to modules, it is shown that, for an R-module M, the class σ[M] of all M-subgenerated modules is mono-correct if and only if M is semisimple, and the class of all weakly M-injective modules is mono-correct if and only if M is locally noetherian. Applying this to the functor ring of R-Mod provides a new proof that R is left pure semisimple if and only if R-Mod is pure-mono-correct. Furthermore, the class of pure-injective Rmodules is always pure-mono-correct, and it is mono-correct if and only if R is von Neumann regular. The dual notion epi-correctness is also considered and it is shown that a ring R is left perfect if and only if the class of all flat R-modules is epi-correct. At the end some open problems are stated. |
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| Date |
2019-06-18T17:44:23Z
2019-06-18T17:44:23Z 2004 |
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| Type |
Article
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| Identifier |
Correct classes of modules / R. Wisbauer // Algebra and Discrete Mathematics. — 2004. — Vol. 3, № 4. — С. 106–118. — Бібліогр.: 18 назв. — англ.
1726-3255 2000 Mathematics Subject Classification: 16D70, 16P40, 16D60. http://dspace.nbuv.gov.ua/handle/123456789/156603 |
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| Language |
en
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| Relation |
Algebra and Discrete Mathematics
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| Publisher |
Інститут прикладної математики і механіки НАН України
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