Glasnik matematički, Vol. 37 No. 2, 2002.
Original scientific paper
Varieties of grupoids with axioms of the form x^{m+1}y = xy and/or xy^{n+1} = xy
Gorgi Cupona
Naum Celakoski
Biljana Janeva
Abstract
The subject of this paper are varieties (M;N) of groupoids defined by the following system of identities
{ xm+1y = xy : m M } { xyn+1 = xy : n N },
where M, N are sets of positive integers. The equation (M;N) = (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 it is shown for finite M and N that: if M and N are nonempty and gcd(M) = gcd(M N), or only one of M and N is nonempty, then the word problem is solvable in (M;N).
Keywords
Groupoids; varieties of groupoids; partial groupoids; free groupoids; word problem
Hrčak ID:
4793
URI
Publication date:
1.12.2002.
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