ACTA MATHEMATICA UNIVERSITATIS COMENIANAE

ACTA MATHEMATICA UNIVERSITATIS COMENIANAE

Vol. 65, 2 (1996)
pp. 189-193

KERNELS OF TOLERANCE RELATIONS
I. CHAJDA, G. CZEDLI and I. G. ROSENBERG

Abstract. Algebras with 0 and their ideals in Gumm and Ursini's sense Ref. \GU, Ref. \U are considered. A variety $\K$ is called \emph$0$-tolerance regular if each tolerance relation $\al$ of any $A\in \K$ is uniquely determined by its kernel $[0]_\al=\set x\in A:\ll 0,x\rr\in \al.$. The main result, strengthening Agliano and Ursini Ref. \AU, asserts that every 0-tolerance regular variety is congruence permutable. Tolerance kernels of single algebras are also considered.

AMS subject classification.
Keywords. Ideal determined, variety, variety with 0, tolerance, kernel, ideal, congruence permutable

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