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Closure operators in modules and adjoint functors, II
Authors: Caşu Alexei
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Abstract
In this work we study the relations between the closure operators of two module categories connected by two adjoint \emph{contravariant} functors. The present article is a continuation of the paper \cite{kas1} (Part~I), where the same question is investigated in the case of two adjoint covariant functors.\\ \noindent\hspace*{6mm}An arbitrary bimodule $_{\ind R}U_{\!\ind S}$ defines a pair of adjoint contravariant functors $H_1 = Hom_{\ind R}(\mbox{-},U) : R\mbox{-Mod} \to \mbox{Mod-}S$ and $H_2 = Hom_{\ind S}(\mbox{-},U) : \mbox{Mod-}S \to R\mbox{-Mod}$ with two associated natural transformations $\Phi : \unu_{\ind {R\mbox{-\tiny Mod}}}\to H_2H_1$ \ and \ $\Psi : \unu_{\ind {\mbox{\tiny Mod-}S}}\to H_1H_2$. In this situation we study the connections between the closure operators of the categories $R\mbox{-Mod}$ and \ $\mbox{Mod-}S$.Institute of Mathematics and Computer Science
Academy of Sciences of Moldova
5 Academiei str. Chisinau, MD−2028
Moldova
E-mail:
Academy of Sciences of Moldova
5 Academiei str. Chisinau, MD−2028
Moldova
E-mail:
Fulltext
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Contents
- Quotient Structure and Chain Conditions on Quasi Modules
- On statistical convergence in generalized Lacunary sequence spaces
- Aspects of stability for multicriteria quadratic problems of Boolean programming
- Solution and full classification of generalized binary functional equations of the type (3;3;0)
- On the solvability of a class of boundary value problems for systems of the integral equations with power nonlinearity on the whole axis
- Isohedral tilings by 8-, 10- and 12-gons for hyperbolic translation group of genus two
- Some properties of left-transitive quasigroups
- General Method for Defining Finite Non-commutative Associative Algebras of Dimension m>1
- Closure operators in modules and adjoint functors, II
- Later developments based on some ideas of Andrunachievici: Special radicals and The Lemma
- Corrigendum to "The multiplicative Zagreb co-indices on two graph operators" Bul. Acad. Științe Repub. Mold. Mat., 2016, no. 2(81), 18-26
