Vol. 38, No. 2, 1971

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Subalgebra systems of powers of partial universal algebras

A. A. Iskander

Vol. 38 (1971), No. 2, 457–463

A set A and an integer n > 1 are given. S is any family of subsets of An. Necessary and sufficient conditions are found for the existence of a set F of finitary partial operations on A such that S is the set of all subalgebras of A;Fn. As a corollary, a family E of equivalence relations on A is the set of all congruences on A;Ffor some F if and only if E is an algebraic closure system on A2.

Mathematical Subject Classification
Primary: 08A25
Received: 20 January 1970
Published: 1 August 1971
A. A. Iskander