MODULE HOMOMORPHISMS OF GROUP ALGEBRAS OF CYCLIC p-GROUPS IN CHARACTERISTIC p

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International Electronic Journal of Algebra
Volume:7 Issue:7
MODULE HOMOMORPHISMS OF GROUP ALGEBRAS OF CYCLIC p-GROUPS IN CHARACTERISTIC p

MODULE HOMOMORPHISMS OF GROUP ALGEBRAS OF CYCLIC p-GROUPS IN CHARACTERISTIC p

Authors : Vahid Shirbisheh

Pages : 59-77

View : 21 | Download : 9

Publication Date : 2010-06-01

Article Type : Research Paper

Abstract :Given a prime number p, we study the module theory of F[G], where F is a field of characteristic p and G is a cyclic p-group. We describe a construction of the set of all injective homomorphisms between two finitely generated F[G]-modules in terms of their numerical invariants. We also give a conceptual characterization of injective F[G]-homomorphisms. Finally, we characterize all submodules of a given finitely generated F[G]-module. These results were applied to describe all solutions of a specific type of Galois embedding problems in [8].
Keywords : module theory, group algebras, cyclic p groups, Galois embedding problems

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