Restricted congruence regularity of algebras
Acta mathematica Universitatis Comenianae, Tome 71 (2002) no. 1
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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".