Titlebook: Classically Semisimple Rings; A Perspective Throug Martin Mathieu Textbook 2022 The Editor(s) (if applicable) and The Author(s), under excl

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Motivation from Ring Theory,stances where the setting of Ring Theory in its strictest sense turns out to be too narrow, or at least somewhat cumbersome, in order to provide us with enough tools for studying certain properties of rings. We shall take this as part of our motivation to introduce the more comprehensive setting of modules below.

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Semiprimitivity of Group Rings,g .[.] is semisimple, provided . is a finite group. For any field ., the elements of . form a basis of the .-vector space .[.] and if the ring .[.] is semisimple, then it is necessarily Artinian, hence finite dimensional (Corollary . and Exercise .). As a result, we cannot expect .[.] to be semisimple for an infinite group ..

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d biographical sketches of important figures scattered throughout the text..Assuming previous knowledge in linear and basic abstract algebra, this book can serve as a textbook for a course in algebra, providing students with valuable early exposure to category theory..978-3-031-14208-6978-3-031-14209-3

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