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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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