منابع مشابه
Separable Algebras over Commutative Rings
Introduction. The main objects of study in this paper are the commutative separable algebras over a commutative ring. Noncommutative separable algebras have been studied in [2]. Commutative separable algebras have been studied in [1] and in [2], [6] where the main ideas are based on the classical Galois theory of fields. This paper depends heavily on these three papers and the reader should con...
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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 t...
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Let $R$ be a commutative ring with identity and let $M$ be an $R$-module. In this paper we introduce a new graph associated to modules over commutative rings. We study the relationship between the algebraic properties of modules and their associated graphs. A topological characterization for the completeness of the special subgraphs is presented. Also modules whose associated graph is complete...
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Suppose G is an abelian group and R is a commutative ring with 1 of char(R) = 0. It is proved that if G is R-favorable torsion and RH and RG are R-isomorphic group algebras for some group H , then H is Rfavorable torsion abelian if and only if either inv(R) = ∅ or inv(R) = ∅ and R is an ND-ring. This strengthens results due to W. Ullery (Comm. Algebra, 1986), (Rocky Mtn. J. Math., 1992) and (Co...
متن کاملDuality and Rational Modules in Hopf Algebras over Commutative Rings
Let A be an algebra over a commutative ring R. If R is noetherian and A◦ is pure in R, then the categories of rational left A-modules and right A◦-comodules are isomorphic. In the Hopf algebra case, we can also strengthen the Blattner– Montgomery duality theorem. Finally, we give sufficient conditions to get the purity of A◦ in R. © 2001 Academic Press
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 1966
ISSN: 0002-9947
DOI: 10.2307/1994561