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