A note on local polynomial functions on commutative semigroups

Journal of the Australian Mathematical Society

P. A. Grossman¹ 

关键词: 08 A 40;    20 M 14;   

DOI  :  10.1017/S1446788700017602

学科分类：数学（综合）

来源: Cambridge University Press

【 摘 要 】

Given a universal algebra A, one can define for each positive integer n the set of functions on A which can be “interpolated” at any n elements of A by a polynomial function on A. These sets form a chain with respect to inclusion. It is known for several varieties that many of these sets coincide for all algebras A in the variety. We show here that, in contrast with these results, the coincident sets in the chain can to a large extent be specified arbitrarily by suitably choosing A from the variety of commutative semigroups.

【 授权许可】

Unknown