Adjoint functors, preradicals and closure operators in module categories
In this article preradicals and closure operators are studied in an adjoint situation, defined by two covariant functors between the module categories R-Mod and S-Mod. The mappings which determine the relationship between the classes of preradicals and the classes of closure operators of these categ...
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| Published in: | Algebra and Discrete Mathematics |
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| Date: | 2019 |
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| Format: | Article |
| Language: | English |
| Published: |
Інститут прикладної математики і механіки НАН України
2019
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/188493 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Adjoint functors, preradicals and closure operators in module categories / A.I. Kashu // Algebra and Discrete Mathematics. — 2019. — Vol. 28, № 2. — С. 260–277. — Бібліогр.: 11 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| Summary: | In this article preradicals and closure operators are studied in an adjoint situation, defined by two covariant functors between the module categories R-Mod and S-Mod. The mappings which determine the relationship between the classes of preradicals and the classes of closure operators of these categories are investigated. The goal of research is to elucidate the concordance (compatibility) of these mappings. For that some combinations of them, consisting of four mappings, are considered and the commutativity of corresponding diagrams (squares) is studied. The obtained results show the connection between considered mappings in adjoint situation.
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| ISSN: | 1726-3255 |