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Algebra Discrete Math., 2003, Issue 3, Pages 46–53 (Mi adm383)  

This article is cited in 2 scientific papers (total in 2 papers)

RESEARCH ARTICLE

On equivalence of some subcategories of modules in Morita contexts

A. I. Kashu

Str. Academiei,. 5, Inst. of Mathematics and Computer Science,. MD–2028 Chisinau, Rep. of Moldova

Abstract: A Morita context $(R, _RV_S, _SW_R, S)$ defines the isomorphism $\mathcal L_0(R)\cong\mathcal L_0(S)$ of lattices of torsions $r\geq r_I$ of $R$-$Mod$ and torsions $s\geq r_J$ of $S$-$Mod$, where $I$ and $J$ are the trace ideals of the given context. For every pair $(r,s)$ of corresponding torsions the modifications of functors $T^W=W\otimes_{R^-}$ and $T^V=V\otimes_{S^-}$ are considered:
\begin{equation*} R\textrm{-}Mod\supseteq\mathcal P(r) ???????????? \mathcal P(s)\subseteq S\textrm{-}Mod, \end{equation*}
where $\mathcal P(r)$ and $\mathcal P(s)$ are the classes of torsion free modules. It is proved that these functors define the equivalence
\begin{equation*} \mathcal P(r)\cap\mathcal J_I\approx\mathcal P(s)\cap\mathcal J_J, \end{equation*}
where $\mathcal P(r)=\{_RM\mid r(M)=0\}$ and $\mathcal J_I=\{_RM\mid IM=M\}$.

Keywords: torsion (torsion theory), Morita context, torsion free module, accessible module, equivalence.

Full text: PDF file (200 kB)

Bibliographic databases:
MSC: 16S90, 16D90
Received: 04.06.2003
Revised: 27.10.2003
Language:

Citation: A. I. Kashu, “On equivalence of some subcategories of modules in Morita contexts”, Algebra Discrete Math., 2003, no. 3, 46–53

Citation in format AMSBIB
\Bibitem{Kas03}
\by A.~I.~Kashu
\paper On equivalence of some subcategories of modules in Morita contexts
\jour Algebra Discrete Math.
\yr 2003
\issue 3
\pages 46--53
\mathnet{http://mi.mathnet.ru/adm383}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2048639}
\zmath{https://zbmath.org/?q=an:1067.16006}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Pecsi B., “On Morita Contexts in Bicategories”, Appl. Categ. Struct., 20:4 (2012), 415–432  crossref  mathscinet  zmath  isi  scopus
    2. A. I. Kashu, “A survey of results on radicals and torsions in modules”, Algebra Discrete Math., 21:1 (2016), 69–110  mathnet  mathscinet
  • Algebra and Discrete Mathematics
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