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 Diskr. Mat., 2017, Volume 29, Issue 3, Pages 70–91 (Mi dm1453)

Artinian bimodule with quasi-Frobenius bimodule of translations

A. A. Nechaev, V. N. Tsypyscheva

a Moscow Technological University

Abstract: The possibility to generalize the notion of a linear recurrent sequence (LRS) over a commutative ring to the case of a LRS over a non-commutative ring is discussed. In this context, an arbitrary bimodule $_AM_B$ over left- and right-Artinian rings $A$ and $B$, respectively, is associated with the equivalent bimodule of translations $_CM_Z$, where $C$ is the multiplicative ring of the bimodule $_AM_B$ and $Z$ is its center, and the relation between the quasi-Frobenius conditions for the bimodules $_AM_B$ and $_CM_Z$ is studied. It is demonstrated that, in the general case, the fact that $_AM_B$ is a quasi-Frobenius bimodule does not imply the validity of the quasi-Frobenius condition for the bimodule $_CM_Z$. However, under some additional assumptions it can be shown that if $_CM_Z$ is a quasi-Frobenius bimodule, then the bimodule $_AM_B$ is quasi-Frobenius as well. } \keywords{ Quasi-Frobenius bimodule, Artinian ring, multiplicative ring, bimodule of translatios, linear recurrent sequence

Keywords: Quasi-Frobenius bimodule, Artinian ring, multiplicative ring, bimodule of translatios, linear recurrent sequence.

DOI: https://doi.org/10.4213/dm1453

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English version:
Discrete Mathematics and Applications, 2019, 29:2, 103–119

Bibliographic databases:

UDC: 512.552 + 512.553

Citation: A. A. Nechaev, V. N. Tsypyschev, “Artinian bimodule with quasi-Frobenius bimodule of translations”, Diskr. Mat., 29:3 (2017), 70–91; Discrete Math. Appl., 29:2 (2019), 103–119

Citation in format AMSBIB
\Bibitem{NecTsy17} \by A.~A.~Nechaev, V.~N.~Tsypyschev \paper Artinian bimodule with quasi-Frobenius bimodule of translations \jour Diskr. Mat. \yr 2017 \vol 29 \issue 3 \pages 70--91 \mathnet{http://mi.mathnet.ru/dm1453} \crossref{https://doi.org/10.4213/dm1453} \elib{http://elibrary.ru/item.asp?id=29887803} \transl \jour Discrete Math. Appl. \yr 2019 \vol 29 \issue 2 \pages 103--119 \crossref{https://doi.org/10.1515/dma-2019-0010} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000465304800003}