**
ACTA MATHEMATICA UNIVERSITATIS COMENIANAE **

Vol. LXXI, 1(2002)

p. 3

Restricted congruence regularity of algebras

I. Chajda
and
H. Langer

**Abstract**.
An algebra $ \mathcal A $ is called restricted regular with respect to a subset $M$ of its base set if every single class of some congruence $\Theta$ on $ \mathcal A $ determines $\Theta|M$. A variety is called restricted regular with respect to a unary term $t$ if every of its members $(A,F)$ is restricted regular with respect to $t(A)$. The well-known results on (weak) regularity are generalized to the "restricted case".

**AMS subject classification**:
08A30 08B05

**Keywords**:
(weakly) restricted regular algebra, (weakly) restricted
regular variety, Mal'cev type characterization

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