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 SM ISO690:2012KASHU, A.. Preradicals, closure operators in R-Mod and connection between them. In: Algebra and Discrete Mathematics, 2014, vol. 18, pp. 86-96. ISSN 1726-3255. |
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  Algebra and Discrete Mathematics |
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| Volumul 18 / 2014 / ISSN 1726-3255 | ||||||
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| Pag. 86-96 | ||||||
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For a module category R-Mod the class ℙℝ of preradicals and the class ℂO of closure operators are studied. The relations between these classes are realized by three mappings: ϕ : ℂO → ℙℝ and 1,2 : ℙℝ → ℂO. The impact of these mappings on the operations in ℙℝ and ℂO (meet, join, product, coproduct) is investigated. It is established that in most cases the considered mappings preserve the lattice operations (meet and join), while the other two operations are converted one into another (i.e. the product into the coproduct and vice versa). |
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| Cuvinte-cheie Closure operator, lattice, module, Preradical, Product ( coproduct) of closure operators, Ring |
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