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Non commutative rings and applications

Abstract

We intend to continue the research on non commutative rings and applications. The research group has been working in this direction for quitea long time and has already obtained expressive results that are frequently quoted in the literature. The subjects that will be the object of our research in the forth coming period are, among others: the structure of group algebras and its applications to the theory of error-correcting codes. We expect to study the relations among several classes of codes - cyclic, abelian, metabelian, nilpotent, etc. -and to exibit efficient codes constructed in this way; the structure of division rings and, in particular, the existence of free objects (groups, algebras, group algebras) in division rings infinite dimensional over their centers. Apply methods of microlocalization to generalize Cohn's localization theory to graded division rings; study cohomologies based on partial actions and in partial group algebras, the problem of the globalization of partial cohomology, extension of rings related to partial actions, galois theory of partial actions and applications of the theory to semigroups, symbolic dynamics, and other classes of algebras; hopf algebras and their non commutative invariants; rings with polynomial identities, particularly fundamental álgebras and growth problems. (AU)

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