Polynomial functions over commutative semi-groups |
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Authors: | G. Kowol H. Mitsch |
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Affiliation: | (1) Mathematisches Institut der Universität-Wien, Strudlhofgasse 4, A - 1090 Wien, Austria |
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Abstract: | Let S be a commutative semigroup. We consider the semigroup P(S) with respect to composition of all transformations p: S S of the form x a,x xn or x axn (a S; n N) and the semigroup P(S) containing only elements of the last two forms. Since all polynomials over S have the form a, xn or ax these transformations are the so-called polynomial functions over S. We investigate the relationship between the structures of S and(S) resp. P(S) — a criterion on the commutativity of S has been shown by means of polynomial functions in 2. |
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