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 SM ISO690:2012KASHU, A.. Closure operators in the categories of modules Part I (Weakly hereditary and idempotent operators). In: Algebra and Discrete Mathematics, 2013, vol. 15, pp. 213-228. ISSN 1726-3255. |
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  Algebra and Discrete Mathematics |
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| Volumul 15 / 2013 / ISSN 1726-3255 | ||||||
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| Pag. 213-228 | ||||||
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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 FC1 and FC2, which in every module M distinguish the set of C-dense submodules FC1(M) and the set of C-closed submodules FC2 (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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| Cuvinte-cheie Closed submodule, Closure operator, Dense submodule, lattice, Lattice of submodules, module, Preradical, Ring |
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