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Congruence relations of multialgebras. (English) Zbl 0554.08001
A concept of congruence relation and homomorphism for multialgebras is developed as well as the concept of variety of multialgebras and (totally) free multialgebra. Every multialgebra is isomorphic to a subdirect product of subdirectly irreducible multialgebras (Theorem 2.2) and every class of multialgebras of the same type defined by a set of multialgebra implications forms a multialgebra variety (Theorem 3.2).
Reviewer: I.Chajda

MSC:
08A02 Relational systems, laws of composition
08B99 Varieties
08C10 Axiomatic model classes
08B20 Free algebras
08A05 Structure theory of algebraic structures
08A30 Subalgebras, congruence relations
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