Polynomial functions on subdirect products
by
Peter Mayr
JKU Linz, Austria
Coauthors: Kalle Kaarli, University Tartu, Estonia

It is a classical result that the ring of unary polynomial functions on the direct product of commutative rings with identity is isomorphic to the direct product of the polynomial rings on the factors. When we generalize the concept of polynomial functions to arbitrary algebraic structures, this simple correspondence is no longer true. Clearly a polynomial function on an algebra A preserves all congruences and induces polynomial functions on all quotients of A. However, a congruence preserving function that induces polynomials on all subdirectly irreducible quotients is not necessarily polynomial.

Still we can characterize the polynomial functions on certain direct and subdirect products of algebras with Mal'cev term or with majority term by their behaviour on the factors.

Date received: May 14, 2008