Polynomial functions on subdirect products

作     者：Kaarli, Kalle Mayr, Peter 

作者机构：Johannes Kepler Univ Linz Inst Algebra A-4040 Linz Austria Univ Tartu Inst Math EE-50090 Tartu Estonia 

出 版 物：《MONATSHEFTE FUR MATHEMATIK》 (数学月刊)

年 卷 期：2010年第159卷第4期

页      面：341-359页

核心收录：

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

基　　金：Estonian Science Foundation Johannes Kepler Universitat Linz Austrian Science Fund [J2637-N18] University of Colorado at Boulder 

主　　题：Clones of operations Polynomial functions Congruence permutable varieties Congruence distributive varieties 

摘      要：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 x B of finite algebras A and B in a congruence permutable variety has no skew congruences, then the polynomial functions on A x 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 x 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.