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 |
Keywords:
relational system; Horn formula; congruence relation; homomorphism; multialgebras; variety of multialgebras; free multialgebra; subdirect product; subdirectly irreducible multialgebrasReferences:
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