Subalgebra systems of powers of partial universal algebras

A. A. Iskander

Vol. 38 (1971), No. 2, 457–463

DOI: 10.2140/pjm.1971.38.457

Abstract

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;F⟩ⁿ. As a corollary, a family E of equivalence relations on A is the set of all congruences on ⟨A;F⟩ for some F if and only if E is an algebraic closure system on A².

Mathematical Subject Classification

Primary: 08A25

Milestones

Received: 20 January 1970

Published: 1 August 1971