EMIS ELibM Electronic Journals PUBLICATIONS DE L'INSTITUT MATHÉMATIQUE (BEOGRAD) (N.S.)
Vol. 68(82), pp. 59--66 (2000)

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Rectangular loops

Aleksandar Krapez

Matematicki institut SANU, Beograd, Yugoslavia

Abstract: Rectangular groups i.e. direct products of rectangular bands and groups play a significant role in the semilattice decomposition theory of semigroups. In our attempt to generalize this theory to groupoids, we start by investigating {\it rectangular loops\/} i.e. direct products of rectangular bands and loops. \par The standard method of R. A. Knoebel gives us an axiom system for rectangular loops consisting of 21 identities in an extended language. We give a simpler and more intuitive equivalent system of only 12 identities. \par Other important properties of rectangular loops are derived.

Keywords: groupoid, rectangular loop, axiomatization, axiom independence, word problem

Classification (MSC2000): 20N02

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Electronic fulltext finalized on: 1 Nov 2001. This page was last modified: 6 Feb 2002.

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