Closure operators in the categories of modules Part II (Hereditary and cohereditary operators)
This work is a continuation of the paper [1] (Part I), in which the weakly hereditary and idempotent closure operators of the category \(R\)-Mod are described. Using the results of [1], in this part the other classes of closure operators \(C\) are characterized by the associated functions \(\mathcal...
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| Date: | 2018 |
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| Main Author: | |
| Format: | Article |
| Language: | English |
| Published: |
Lugansk National Taras Shevchenko University
2018
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| Subjects: | |
| Online Access: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/757 |
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| Journal Title: | Algebra and Discrete Mathematics |
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Algebra and Discrete Mathematics| Summary: | This work is a continuation of the paper [1] (Part I), in which the weakly hereditary and idempotent closure operators of the category \(R\)-Mod are described. Using the results of [1], in this part the other classes of closure operators \(C\) are characterized by the associated functions \(\mathcal{F}_1^C\) and \(\mathcal{F}_2^{C}\) which separate in every module \(M \in R\)-Mod the sets of \(C\)-dense submodules and \(C\)-closed submodules. This method is applied to the classes of hereditary, maximal, minimal and cohereditary closure operators. |
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