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Retracts and \(Q\)-independence. (English) Zbl 1131.08003
Summary: A non-empty set \(X\) of a carrier \(A\) of an algebra \(\mathbf A\) is called \(Q\)-independent if the equality of two term functions \(f\) and \(g\) of the algebra \(\mathbf A\) on any finite system of elements \(a_1,a_2,\dots,a_n\) of \(X\) implies \(f(p(a_1),p(a_2),\dots,p(a_n)) = g(p(a_1),p(a_2),\dots,p(a_n))\) for any mapping \(p\in Q\). An algebra \(\mathbf B\) is a retract of \(\mathbf A\) if \(\mathbf B\) is the image of a retraction (i.e. of an idempotent endomorphism of \(\mathbf B\)). We investigate \(Q\)-independent subsets of algebras which have a retraction in their set of term functions.
MSC:
08B20 Free algebras
08A40 Operations and polynomials in algebraic structures, primal algebras
06D15 Pseudocomplemented lattices
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