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http://hdl.handle.net/123456789/137
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DC Field | Value | Language |
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dc.contributor.author | Wisbauer, Robert | - |
dc.date.accessioned | 2015-11-11T12:25:12Z | - |
dc.date.available | 2015-11-11T12:25:12Z | - |
dc.date.issued | 2004 | - |
dc.identifier.issn | 1726-3255 | - |
dc.identifier.uri | http://hdl.handle.net/123456789/137 | - |
dc.description.abstract | 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 [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 R-modules 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. | uk_UA |
dc.language.iso | en | uk_UA |
dc.publisher | Луганский национальный университет им. Т. Шевченко | uk_UA |
dc.subject | алгебра | uk_UA |
dc.title | Correct classes of modules | uk_UA |
dc.type | Article | uk_UA |
Appears in Collections: | Статті |
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adm-n4-8.pdf | 169.62 kB | Adobe PDF | View/Open |
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