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Diskr. Mat., 2011, Volume 23, Issue 1, Pages 84–93 (Mi dm1132)  

On the semigroups of endomorphisms of direct products of commutative Moufang loops

N. T. Lupasço, N. I. Sandu


Abstract: In this paper it is proved that the semigroup of endomorphisms of a commutative Moufang loop (CML) which admits a decomposition into the direct product of its subloops is isomorphic to the semigroup of $M,M$-matrices. We introduce the notion of the holomorph of a CML which admits a direct decomposition and give the matrix representation of the holomorph.

DOI: https://doi.org/10.4213/dm1132

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English version:
Discrete Mathematics and Applications, 2011, 21:1, 79–90

Bibliographic databases:

UDC: 512.48
Received: 08.11.2007

Citation: N. T. Lupasço, N. I. Sandu, “On the semigroups of endomorphisms of direct products of commutative Moufang loops”, Diskr. Mat., 23:1 (2011), 84–93; Discrete Math. Appl., 21:1 (2011), 79–90

Citation in format AMSBIB
\Bibitem{LupSan11}
\by N.~T.~Lupas{\c c}o, N.~I.~Sandu
\paper On the semigroups of endomorphisms of direct products of commutative Moufang loops
\jour Diskr. Mat.
\yr 2011
\vol 23
\issue 1
\pages 84--93
\mathnet{http://mi.mathnet.ru/dm1132}
\crossref{https://doi.org/10.4213/dm1132}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2830699}
\elib{http://elibrary.ru/item.asp?id=20730375}
\transl
\jour Discrete Math. Appl.
\yr 2011
\vol 21
\issue 1
\pages 79--90
\crossref{https://doi.org/10.1515/DMA.2011.006}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-79953304110}


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