## A common generalization of permutability and 0-permutability.(English)Zbl 1038.08004

Summary: We present a congruence property which is a common generalization of congruence permutability and $$0$$-permutability. We characterize varieties of algebras satisfying this property by a Mal’tsev-type condition as well as by a relational condition. Examples of such varieties are included.

### MSC:

 08B05 Equational logic, Mal’tsev conditions 08A30 Subalgebras, congruence relations

### Keywords:

congruence permutability; $$0$$-permutability; varieties
Full Text:

### References:

 [1] Bělohlávek R., Chajda I.: The intermediate property between local permutability and permutability. General Algebra and Applications, Proc. of the 59th Workshop on General Algebra, Potsdam, 2000 (Shaker Verlag), 19-24. [2] Gumm H.-P., Ursini A.: Ideals in universal algebras. Algebra Universalis 19 (1984), 45-54. · Zbl 0547.08001 [3] Mal’cev A. I.: On the general theory of algebraic systems. Matem. Sbornik 35 (1954), 3-20) [4] Werner H.: A Mal’cev condition for admissible relations. Algebra Universalis 3 (1973), 263. · Zbl 0276.08004
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.