Algebras and varieties satisfying the congruence extension property. (English) Zbl 0768.08005

Chajda, Ivan

Acta Sci. Math. 56, No. 1-2, 19-21 (1992).

Necessary and sufficient term conditions are given under which a variety has CEP. An algebra \(A\) satisfies strong CEP if for any subalgebra \(B\) of \(A\) and each \(\Theta\in\text{Con }B\) there exists \(\Phi\in\text{Con }A\) such that \([b]_ \Theta=[b]_ \Phi\) for each \(b\in B\). If \(A\) satisfies strong CEP then it is Hamiltonian. For a variety, these conditions are equivalent.

Reviewer: I.Chajda (Přerov)

MSC:

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

Keywords:

congruence extension property; Hamiltonian algebra; strong CEP