Let k be a field, G an abelian group with a bicharacter, A a colour algebra; i.e., an associative graded k-algebra with identity, C a graded A-coring that is projective as a right A-module, C∗ the graded dual ring of C and Λ a left graded C-comodule that is finitely generated as a graded right C∗-module. We give necessary and sufficient conditions for projectivity and flatness of a graded modul...

A Morita context is constructed for any comodule of a coring and, more generally, for an L-C bicomodule Σ for a coring extension (D : L) of (C : A). It is related to a 2-object subcategory of the category of k-linear functors M → M. Strictness of the Morita context is shown to imply the Galois property of Σ as a C-comodule and a Weak Structure Theorem. Sufficient conditions are found also for a...

In this paper we construct a cylindrical module A♮H for an Hcomodule algebra A, where the antipode of the Hopf algebra H is bijective. We show that the cyclic module associated to the diagonal of A♮H is isomorphic with the cyclic module of the crossed product algebra A ⋊H. This enables us to derive a spectral sequence for the cyclic homology of the crossed product algebra. We also construct a c...

T. Shudo and H. Miyamito [3] showed that C can be decomposed into a direct sum of its indecomposable subcoalgebras of C. Y.H. Xu [5] showed that the decomposition was unique. He also showed that M can uniquely be decomposed into a direct sum of the weak-closed indecomposable subcomodules of M(we call the decomposition the weak-closed indecomposable decomposition ) in [6]. In this paper, we give...