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Closure operators in the categories of modules. Part I (Weakly hereditary and idempotent operators)
In this work the closure operators of a category of modules R-Mod are studied. Every closure operator C of R-Mod defines two functions F₁с and F₂с, which in every module M distinguish the set of C-dense submodules F₁с(M) and the set of C-closed submodules F₂с(M). By means of these functions three ty...
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| Main Author: | |
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| Format: | Article |
| Language: | English |
| Published: |
Інститут прикладної математики і механіки НАН України
2013
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| Series: | Algebra and Discrete Mathematics |
| Online Access: | http://dspace.nbuv.gov.ua/handle/123456789/152290 |
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| Summary: | In this work the closure operators of a category of modules R-Mod are studied. Every closure operator C of R-Mod defines two functions F₁с and F₂с, which in every module M distinguish the set of C-dense submodules F₁с(M) and the set of C-closed submodules F₂с(M). By means of these functions three types of closure operators are described: 1) weakly hereditary; 2) idempotent; 3) weakly hereditary and idempotent. |
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