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S. S. Marchenkov

On the structure of equationally closed classes

We study the structure of equationally closed classes. We prove a theorem on representation of the graph of a function in an equationally closed class in the form of a union of the sets of values of special vector functions. For any k ≥ 2 we establish the equational generability of any equationally closed class in P_k by the set of all its k-place functions. We find all equationally precomplete classes in P_k and prove a criterion of equational completeness. Some results are extended from equationally closed classes to positively closed classes.

Discrete Mathematics and Applications, Walter de Gruyter

Print ISSN: 0924-9266
Volume: 16, 12/2006
Pages: 563 - 576

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