Varieties of groupoids with axioms of the form x^m+1y=xy and/or xyⁿ⁺¹=xy
by
Biljana Janeva
Institute of Informatics, Faculty of Natural Sciences and Mathematics, Skopje, Republic of Macedonia
Coauthors: \' Gorgi Cupona (Macedonian Academy of Sciences and Arts, Skopje, Republic of Macedonia), Naum Celakoski (Faculty of Mechanical Engeneering, Skopje, Republic of Macedonia)

The subject of this paper are varieties U(M, N) of groupoids defined by the following system of identities:

{ xm+1y=xy: m in M} \cup { xyn+1y=xy: n in N},

where, M, N are sets of positive integers such that M \cup N =/= \emptyset. The equation U(M, N) = U(M', N') for any given pair (M, N) is solved, and, among all solutions, one called canonical, is singled out. Applying a result of Evans ("The Word Problem for Abstract Algebras", J. London Math. Soc 26 (1951)), it is shown that, if M and N are finite nonempty and gcd(M)=gcd(M \cup N), or exactly one of the sets M, N is nonempty and finite, then the word problem is solvable in U(M, N).

Date received: March 20, 2000

Copyright © 2000 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caex-42.