Geodesic
Preradical and kernel functors over categories of $S$-acts
Algebra and discrete mathematics, Tome 10 (2010) no. 1, pp. 57-66

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We concider the big lattices of preradicals and kernel functors over some cathegories of centered $S$-acts, where $S$ is monoid whit zero. We prove that those big lattices are two elements if and only if monoid $S$ is groups with zero. A subset of a Rees generated pretorsion theory is a subquantale of quantale of pretorsion theory.
Keywords: monoids, $S$-acts, preradical, quasi-filter. 
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Mykola Komarnitskiy; Roman Oliynyk. Preradical and kernel functors over categories of $S$-acts. Algebra and discrete mathematics, Tome 10 (2010) no. 1, pp. 57-66. http://geodesic.mathdoc.fr/item/ADM_2010_10_1_a5/