TERM REWRITING SYSTEM FOR SOLVING THE WORD PROBLEM FOR STEINER LOOPS

Abstract

The variety of Steiner loops (or sloops) consists of algebras of type \(<2,0>\) satisfying the laws (S1), (S2) and (S3). It is shown in [7] that the word problem for the variety of sloops is solvable, but that proof is obtained as a consequence of a theorem of T. Evans [3]. Here we use a direct approach, i.e. we define a term rewriting system that solves the word problem for sloops, in such a way obtaining a more effective algorithm than that given in [3].