Polynomial Maps of Modules

Details Polynomial Maps of Modules Polynomial Maps of Modules

2011-12-05

arxiv.org/abs/1112.0991v1

Mathematics

Rings and Algebras

Scientific paper

The article focuses on three different notions of polynomiality for maps of modules. In addition to the polynomial maps studied by Eilenberg and Mac Lane, and the strict polynomial maps ("lois polynomes") considered by Roby, we introduce numerical maps of modules and investigate their properties. Even though our notion require the existence of binomial coefficients in the base ring, we argue that it constitutes the correct way to generalise Eilenberg and Mac Lane's original definition, of polynomial maps on abelian groups, to modules over more general rings. The main theorem propounds that our maps admit a description word by word corresponding to Roby's definition of strict polynomial maps.

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