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010   $a9783031142093$b(electronic bk.)
010   $z9783031142086
024 7 $a10.1007/978-3-031-14209-3
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035   $a(PPN)267816634
035   $a(OCoLC)1357017227
035   $a(DE-He213)978-3-031-14209-3
035   $a(EXLCZ)9925913866300041
100   $a20221219d2022      u|         0
101 0 $aeng
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181   $ctxt$2rdacontent
182   $cc$2rdamedia
183   $acr$2rdacarrier
200 10$aClassically Semisimple Rings $eA Perspective Through Modules and Categories /$fby Martin Mathieu
205   $a1st ed. 2022.
210  1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2022.
215   $a1 online resource (159 pages)
225 1 $aMathematics and Statistics Series
311 08$aPrint version: Mathieu, Martin Classically Semisimple Rings Cham : Springer International Publishing AG,c2022 9783031142086 
320   $aIncludes bibliographical references and index.
327   $aIntroduction -- Chapter 1. Motivation from Ring Theory -- Chapter 2. Constructions with Modules -- Chapter 3. The Isomorphism Theorems -- Chapter 4. Noetherian Modules -- Chapter 5. Artinian Modules -- Chapter 6. Simple and Semisimple Modules -- Chapter 7. The Artin-Weddeburn Theorem -- Chapter 8. Tensor Products of Modules -- Chapter 9. Exchange Modules and Exchange Rings -- Chapter 10. Semiprimitivity of Group Rings -- Bibliography -- Index of Symbols -- Index. .
330   $aClassically Semisimple Rings is a textbook on rings, modules and categories, aimed at advanced undergraduate and beginning graduate students. The book presents the classical theory of semisimple rings from a modern, category-theoretic point of view. Examples from algebra are used to motivate the abstract language of category theory, which then provides a framework for the study of rings and modules, culminating in the Wedderburn?Artin classification of semisimple rings. In the last part of the book, readers are gently introduced to related topics such as tensor products, exchange modules and C*-algebras. As a final flourish, Rickart?s theorem on group rings ties a number of these topics together. Each chapter ends with a selection of exercises of varying difficulty, and readers interested in the history of mathematics will find biographical sketches of important figures scattered throughout the text. Assuming previous knowledge in linear and basic abstract algebra, this book can serve as a textbook for a course in algebra, providing students with valuable early exposure to category theory.
410  0$aMathematics and Statistics Series
606   $aMathematics
606   $aAlgebra
606   $aCommutative algebra
606   $aCommutative rings
606   $aAlgebra, Homological
606   $aMathematics
606   $aAlgebra
606   $aCommutative Rings and Algebras
606   $aCategory Theory, Homological Algebra
615  0$aMathematics.
615  0$aAlgebra.
615  0$aCommutative algebra.
615  0$aCommutative rings.
615  0$aAlgebra, Homological.
615 14$aMathematics.
615 24$aAlgebra.
615 24$aCommutative Rings and Algebras.
615 24$aCategory Theory, Homological Algebra.
676   $a512.4
676   $a512.4
700   $aMathieu$b Martin$01273316
801  0$bMiAaPQ
801  1$bMiAaPQ
801  2$bMiAaPQ
912   $a9910637742003321
996   $aClassically Semisimple Rings$93000277
997   $aUNINA