On composition of polynomials (Q1240747)

In this paper the order of enlargeability \(\varepsilon(A)\) 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 \[ \varepsilon(a):=\min \{n:\forall_B([A^{(n)}=B^{(n)}]\Rightarrow[A^{(\omega)}\supseteq B^{(\omega)}])\}, \] where min \(\{\emptyset\}:=\infty\). \(\varepsilon(A)\) is determined for algebras \(A\) over countable and uncountable fields \(F\). Special results are obtained for \(A = F\).