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Structure of free algebras. (English) Zbl 0704.08006
Let F(X) be a free algebra in a variety, and let $$(x_ 1,x_ 2,...,x_ n)\omega$$ be a term, $$x_ 1,x_ 2,...,x_ n\in X$$. This term is strongly returnable if for arbitrary $$x\in X$$ there exists a term (x,y)$$\pi$$ such that $$(x,(x_ 1,...,x_ n)\omega)\pi =x$$. The author defines weaker forms of returnability and discusses some basic properties of these notions.
Reviewer: E.T.Schmidt
##### MSC:
 08B20 Free algebras 08A40 Operations and polynomials in algebraic structures, primal algebras
##### Keywords:
returnable term; free algebra
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##### References:
 [1] G. Grätzer: Universal algebra. London 1968. · Zbl 0182.34201
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