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Universal varieties of distributive double p-algebras. (English) Zbl 0574.06009

A category C is called (a) universal, if any full category of algebras is isomorphic to a full subcategory of C. (b) iso-universal, if, for any full category of algebras A, Iso(A) is isomorphic to a full subcategory of Iso(C).
Answering a question of E. Fried, the authors exhibit a finitely generated universal variety of distributive double p-algebras. They also show that the following are equivalent for any finitely generated variety V of distributive double p-algebras: (i) V is not congruence permutable, (ii) V contains a subdirectly irreducible algebra which is not simple, (iii) The variety of double Stone algebras is contained in V, (iv) V is iso-universal.
Reviewer: I.Düntsch

MSC:

06D15 Pseudocomplemented lattices
08C05 Categories of algebras
08B99 Varieties
06B20 Varieties of lattices
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