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By Tomasz Brzezinski, José Luis Gomez-Pardo, Ivan Shestakov, Patrick F. Smith

The 23 articles during this quantity surround the complaints of the International convention on Modules and Comodules held in Porto (Portugal) in 2006 and devoted to Robert Wisbauer at the party of his sixty fifth birthday. those articles replicate Professor Wisbauer's vast pursuits and provides an outline of other fields concerning module idea, a few of that have a protracted culture while others have emerged lately. They comprise themes within the formal concept of modules bordering on classification idea, in ring thought, in Hopf algebras and quantum teams, and in corings and comodules.

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The most goal of those lectures is first to in short survey the basic con­ nection among the illustration concept of the symmetric workforce Sn and the idea of symmetric features and moment to teach how combinatorial equipment that come up clearly within the concept of symmetric capabilities bring about effective algorithms to specific a number of prod­ ucts of representations of Sn when it comes to sums of irreducible representations.

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We refer to the Appendix for the definitions of generic datum and U (D); see [AS3] for a detailed exposition. The general scheme of the proof is exactly the same as for the proof of [AS3, Th. 2], an analogous theorem but assuming “positive” instead of “generic” infinitesimal braiding. The main new feature is the following result. 2. Let (V, c) be a finite-dimensional braided vector space with generic braiding. Then the following are equivalent: (a) B(V ) has finite Gelfand-Kirillov dimension. (b) (V, c) is twist-equivalent to a braiding of DJ-type with finite Cartan matrix.

G´omezTorrecillas [C-IG-T1995] and [C-IG-T1996] as an extension of classical Morita contexts to Abelian categories. 3. Let A and B be Abelian categories. A right (left) wide Morita context between A and B is a datum Wr = (G, A, B, F, η, ρ), where G : A B:F are right (left) exact covariant functors and η : F ◦ G −→ 1A , ρ : G ◦ F −→ 1B (η : 1A −→ F ◦ G, ρ : 1B −→ G ◦ F ) are natural transformations, such that for every pair of objects (A, B) ∈ A × B the compatibility conditions G(ηA ) = ρG(A) and F (ρB ) = ηF (B) hold.

W is injective. Consequently, the induced right wide Morita context Wr (M) is injective. Acknowledgement The authors thank the referee for his/her careful reading of the paper and for the fruitful suggestions, comments and corrections, which helped in improving several parts of the paper. Moreover, they acknowledge the excellent research facilities as well as the support of their respective institutions, King Fahd University of Petroleum and Minerals and King AbdulAziz University. D. Abrams, Morita equivalence for rings with local units, Comm.

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