Zentralblatt MATH

Publications of (and about) Paul Erdös
Zbl.No:  364.08006
Autor:  Erdös, Paul; Fajtlowicz, Siemion
Title:  On composition of polynomials. (In English)
Source:  Algebra Univers. 7, 357-360 (1977).
Review:  In this paper the order of enlargeability \epsilon(A) of an algebra A over a field F is investigated. Let A(n) denote the set of all n-ary polynomial operations of A and A(\omega) the set of all polynomial operations of A, then

\epsilon(a): = max {n: \forallB([A(n) = B(n)] ==> [A(\omega)\supseteq B(\omega)])},

where min {Ø}: = oo. \epsilon(A) is determined for algebras A over countable and uncountable fields F. Special results are obtained for A = F.
Reviewer:  W .B.Müller
Classif.:  * 08A99 Universal algebra
                   12E99 General field theory

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