ACTA issues

Congruences and ideals in semiloops

R. Bělohlávek, I. Chajda

Acta Sci. Math. (Szeged) 59:1-2(1994), 43-47

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.)