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On a strong property of the weak subalgebra lattice. (English) Zbl 0936.08002
Let \(A\) be a total and locally finite unary algebra of a finite type and \(B\) be a unary partial algebra of the same type. It is proved that if the weak subalgebra lattices of \(A\) and \(B\) are isomorphic, then the strong subalgebra lattices of \(A\) and \(B\) are also isomorphic and, moreover, \(B\) is also total and locally finite.
Reviewer: I.Chajda (Olomouc)

MSC:
08A30 Subalgebras, congruence relations
08A60 Unary algebras
08A55 Partial algebras
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