Dual coalgebras of algebras over commutative rings

[摘要] In the study of algebraic groups the representative functions related to monoid algebras over fields provide an important tool which also yields the finite dual coalgebra of any algebra over a field. The purpose of this note is to transfer this basic construction to monoid algebras over commutative rings R. As an application we obtain a bialgebra (Hopf algebra) structure on the finite dual of the polynomial ring R[x] over a noetherian ring R. Moreover, we give a sufficient condition for the finite dual of any R-algebra A to become a coalgebra. In particular, this condition is satisfied provided R is noetherian and hereditary. (C) 2000 Elsevier Science B.V. All rights reserved.

[发布日期] 2000-10-25