Geodesic
Preradicals, closure operators in $R$-Mod and connection between them
Algebra and discrete mathematics, Tome 18 (2014) no. 1, pp. 86-96

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For a module category $R$-Mod the class $\mathbb{PR}$ of preradicals and the class $\mathbb{CO}$ of closure operators are studied. The relations between these classes are realized by three mappings: $\Phi : \mathbb{CO} \to \mathbb{PR}$ and $\Psi_1, \Psi_2 : \mathbb{PR} \to \mathbb{CO}$. The impact of these mappings on the operations in $\mathbb{PR}$ and $\mathbb{CO}$ (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).
Keywords: ring, lattice, preradical, closure operator, product (coproduct) of closure operators.
Mots-clés : module 
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     author = {A. I. Kashu},
     title = {Preradicals, closure operators in $R${-Mod} and connection between them},
     journal = {Algebra and discrete mathematics},
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     publisher = {mathdoc},
     volume = {18},
     number = {1},
     year = {2014},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ADM_2014_18_1_a8/}
}
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A. I. Kashu. Preradicals, closure operators in $R$-Mod and connection between them. Algebra and discrete mathematics, Tome 18 (2014) no. 1, pp. 86-96. http://geodesic.mathdoc.fr/item/ADM_2014_18_1_a8/