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Название: Group Representation Theory: Modular Representation Theory
Автор: Dornhoff L.
This book presupposes knowledge of only several basic topics in algebra. These include the Sylow theorems and the structure of finite abelian groups from group theory; the structure of finitely generated modules over principal ideal domains; the notion of tensor product of modules over noncommutative rings; and occasionally basic Galois theory of fields. In Part A, we begin by developing the structure theory for semisimple rings with unit. In Part B. we build the broad algebraic foundation needed for modular representation theory without assuming any knowledge of valuation theory. Indeed, we begin with a basic study of chain conditions for modules and the radical of a ring with unit.