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Algebra Logika, 2014, Volume 53, Number 4, Pages 451–465 (Mi al645)  

Representation of some finite rings by matrices over commutative rings

A. Mekei, L. Oyuuntsetseg

The Institute of Mathematics, National University of Mongolia, Ulan Bator, Mongolia

Abstract: We give a complete description of subdirectly irreducible finite associative rings with commuting nilpotent elements. Also it is proved that a finite ring the nilpotent elements of which commute is representable by matrices over a commutative ring.

Keywords: Galois ring, subdirectly irreducible ring, variety of associative rings, representation of finite rings by matrices over commutative rings.

Full text: PDF file (182 kB)
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English version:
Algebra and Logic, 2014, 53:4, 287–297

Bibliographic databases:

UDC: 512.552.4
Received: 17.05.2014
Revised: 10.06.2014

Citation: A. Mekei, L. Oyuuntsetseg, “Representation of some finite rings by matrices over commutative rings”, Algebra Logika, 53:4 (2014), 451–465; Algebra and Logic, 53:4 (2014), 287–297

Citation in format AMSBIB
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\by A.~Mekei, L.~Oyuuntsetseg
\paper Representation of some finite rings by matrices over commutative rings
\jour Algebra Logika
\yr 2014
\vol 53
\issue 4
\pages 451--465
\mathnet{http://mi.mathnet.ru/al645}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3309849}
\transl
\jour Algebra and Logic
\yr 2014
\vol 53
\issue 4
\pages 287--297
\crossref{https://doi.org/10.1007/s10469-014-9291-8}
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