منابع مشابه
Coalgebras Over a Commutative Ring
By a coalgebra over the commutative ring K or a K-coalgebra, we understand a cocommutative, coassociative K-coalgebra with counit. More explicitly we mean a K-module C equipped with maps &C+C&C, subject to the requirement (where we write @ for OK) that the following diagrams commute: CLC@C where the vertical arrow is the one which switches the factors; CAC@C 1 CC38 C@C e@'CtC@C@C, where we have...
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In [2] the notion of “uniformly ideal” was introduced and developed the basic theory. In this article we introduce and advance a theory which, in a sense, dual to that i.e, the notion of “uniformly secondary module”.
متن کاملDual coalgebras of algebras over commutative rings
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...
متن کاملOn Kalman models over a commutative ring
There is a good notion of rational functions with coefficients in a commutative ring. Using this notion, we easily obtain a neat generalization of Chapter 10 of the classical book by Kalman et al. to linear systems over an arbitrary commutative ring. The generalizations certainly exist already. However, we believe that the approach we present is more natural and straightforward. In this note we...
متن کاملOn Fliess models over a commutative ring
Fliess models come as natural generalizations of classical polynomial models (D,N). As known, they are defined in terms of finitely generated modules and provide an adequate description of arbitrary linear systems (not necessarily observable or controllable). In this note we extend Fliess’ approach to linear systems defined over an arbitrary commutative ring. We believe that the exposition will...
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 1974
ISSN: 0021-8693
DOI: 10.1016/0021-8693(74)90161-6