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.

UDC: 512.48

Received: 08.11.2007

DOI: 10.4213/dm1132

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

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