01024nam0-22003491i-450-99000069164040332120160329112217.088.85067.04.2000069164FED01000069164(Aleph)000069164FED0100006916420020821d1983----km-y0itay50------baitaITa-------001yyModello, prototipo, soluzione architettonicaCarlo Aymonino, Claudio Lamanna, Franca PittalugaVeneziaCluva Università1983120 p.ill.30 cmRicerca e didattica4Aymonino,Carlo<1926- >2406Lamanna,ClaudioPittaluga,FrancaITUNINARICAUNIMARCBK99000069164040332101 FA 10845347DINSTARCH C 35313534FARBCDINSTFARBCModello, prototipo, soluzione architettonica324731UNINA03737nam 22006855 450 991063774200332120251113155238.09783031142093(electronic bk.)978303114208610.1007/978-3-031-14209-3(MiAaPQ)EBC7165640(Au-PeEL)EBL7165640(CKB)25913866300041(PPN)267816634(OCoLC)1357017227(DE-He213)978-3-031-14209-3(EXLCZ)992591386630004120221219d2022 u| 0engurcnu||||||||txtrdacontentcrdamediacrrdacarrierClassically Semisimple Rings A Perspective Through Modules and Categories /by Martin Mathieu1st ed. 2022.Cham :Springer International Publishing :Imprint: Springer,2022.1 online resource (159 pages)Mathematics and Statistics SeriesPrint version: Mathieu, Martin Classically Semisimple Rings Cham : Springer International Publishing AG,c2022 9783031142086 Includes bibliographical references and index.Introduction -- 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. .Classically 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.Mathematics and Statistics SeriesMathematicsAlgebraCommutative algebraCommutative ringsAlgebra, HomologicalMathematicsAlgebraCommutative Rings and AlgebrasCategory Theory, Homological AlgebraMathematics.Algebra.Commutative algebra.Commutative rings.Algebra, Homological.Mathematics.Algebra.Commutative Rings and Algebras.Category Theory, Homological Algebra.512.4512.4Mathieu Martin1273316MiAaPQMiAaPQMiAaPQ9910637742003321Classically Semisimple Rings3000277UNINA