Kalle Kaarli, Peter Mayr,
"Polynomial functions on subdirect products"
, in Monatshefte fuer Mathematik, Vol. 159, Nummer 4, Springer, Seite(n) 341-359, 3-2010
Polynomial functions on subdirect products
Sprache des Titels:
A congruence preserving function on a subdirect product of two finite Mal’cev algebras is polynomial if it induces polynomial functions on the subdirect factors and there are no skew congruences between the projection kernels. As a special case, if the direct product A × B of finite algebras A and B in a congruence permutable variety has no skew congruences, then the polynomial functions on A × B are exactly direct products of polynomials on A and on B. These descriptions apply in particular to classical polynomial functions on nonassociative rings. Also, for finite algebras A, B in a variety with majority term, the polynomial functions on A × B are exactly the direct products of polynomials on A and on B. However in arbitrary congruence distributive varieties the corresponding result is not true.