Hyperidentities, hyperequational classes and clone congruences. (English) Zbl 0759.08005

Denecke, K.; Lau, D.; Pöschel, R.; Schweigert, D.

General algebra, Proc. Conf., Vienna/Austria 1990, Contrib. Gen. Algebra 7, 97-118 (1991).

[For the entire collection see Zbl 0731.00007.]
A hyperidentity for a universal algebra \(A\) is an identity \(t=t'\) holding identically in \(A\) for every choice of term functions of \(A\) to represent the operation symbols appearing in \(t\) and \(t'\). Hyperequational classes are classes of algebras of a fixed type which can be defined by hyperidentities. They are also defined equivalently by closure properties. The main results describe various connections between varieties, hyperequational classes, totally invariant congruences on free algebras and fully invariant congruences on clone algebras. The results are used to determine hyperequational subvarieties of varieties generated by two-element algebras.

Reviewer: J.Ježek (Praha)

MSC:

08B05	Equational logic, Mal’tsev conditions
08A30	Subalgebras, congruence relations

Keywords:

hyperidentity; closure properties; hyperequational classes; totally invariant congruences on free algebras; fully invariant congruences on clone algebras; hyperequational subvarieties; varieties generated by two- element algebras

Citations:

Zbl 0731.00007