Abstract. A groupoid $(G;\cdot )$ is left uniquely divisible if for each $a,b\in G$ there exists exactly one $x\in G$ with $a\cdot x=b$. A semiloop is a left uniquely divisible groupoid with a right unit. We characterize ideals of semiloops which are kernels of congruences and we prove that the variety of all semiloops has ideal determined congruences.
AMS Subject Classification
(1991): 08A30, 08B05, 20N05
Keyword(s):
uniquely divisible groupoid,
semiloop,
ideal,
kernel of congruence,
ideal determined congruences
Received June 25, 1991 and in revised form November 29, 1993. (Registered under 5569/2009.)
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