منابع مشابه
A Quasi-hopf Algebra Freeness Theorem
We prove the quasi-Hopf algebra version of the Nichols-Zoeller theorem: A finite-dimensional quasi-Hopf algebra is free over any quasi-Hopf subalgebra.
متن کاملProjectivity and freeness over comodule algebras
Let H be a Hopf algebra and A an H-simple right H-comodule algebra. It is shown that under certain hypotheses every (H,A)-Hopf module is either projective or free as an A-module and A is either a quasi-Frobenius or a semisimple ring. As an application it is proved that every weakly finite (in particular, every finite dimensional) Hopf algebra is free both as a left and a right module over its f...
متن کاملFreeness of the Quantum Coordinate Algebras
The main purpose of this note is to prove that the quantum coordinate algebra A[U ] is free over the ring A = Z[v, v−1]. In [L1], Lusztig defined the quantum coordinate algebra over Q[v, v−1] and prove that it is free as Q[v, v−1]-module. In [APW], Andersen, Polo, and Wen defined the quantum coordinate algebra over the ring A(p,v−1) and proved that the coordinate algebra is free. The main idea ...
متن کاملFreeness Conditions for 2-Crossed Modules of Commutative Algebras
In this paper we give a construction of free 2-crossed modules. By the use of a `step-by-step' method based on the work of Andr e, we will give a description of crossed algebraic models for the steps in the construction of a free simplicial resolution of an algebra. This involves the introduction of the notion of a free 2-crossed module of algebras.
متن کاملSufficient Conditions for the Projective Freeness of Banach Algebras
Let R be a unital semi-simple commutative complex Banach algebra, and let M(R) denote its maximal ideal space, equipped with the Gelfand topology. Sufficient topological conditions are given on M(R) for R to be a projective free ring, that is, a ring in which every finitely generated projective R-module is free. Several examples are included, notably the Hardy algebra H∞(X) of bounded holomorph...
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 2000
ISSN: 0021-8693
DOI: 10.1006/jabr.2000.8363