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A new product of algebras and a type reduction theorem. (English) Zbl 0543.08005
For every finite similarity type T there is constructed an isomorphism F of the category of T-algebras with a full subcategory of the category of groupoids with the following properties: (1) F(A) is finite iff A is finite; (2) F(A) is finitely based iff A is finitely based; (3) \(End(F(A))\simeq End(A);\quad Sub(F(A))\simeq Sub(A);\quad Con(F(A))\simeq 1\oplus Con(A).\) A new product operation, applicable to two algebras of different similarity types, is introduced, used in the construction of F and also studied separately.
Reviewer: J.Ježek

MSC:
08B05 Equational logic, Mal’tsev conditions
08C05 Categories of algebras
08A40 Operations and polynomials in algebraic structures, primal algebras
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