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 frequentlyquoted in the literature.The subjects that will be the object of our research in the forthcomingperiod are, among others:* The structure of group algebras and its applications to the Theoryof Error-Correcting Codes. We expect to study the relations amongseveral 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 freeobjects (groups, algebras, group algebras) in division rings infinite dimensional over their centers. Apply methods of microlocalization togeneralize 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,extensionof rings related to partial actions, Galois Theory of partial actions andapplications of the theory to semigroups, symbolic dynamics, and otherclasses of algebras.* Hopf algebras and their non commutative invariants.* Rings with polynomial identities, particularly fundamental algebrasand growth problems. (AU)
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