01472nam0 2200301 i 450 SUN005485220180621112819.191978-04-86272-89-40.0020061025d1992 |0engc50 baengUS|||| |||||*Greek mathematical thought and the origin of algebraJacob Kleintranslated by Eva BrannNew edNew YorkDover1992XV, 360 p.21 cm.001SUN00235662001 Dover books on advanced mathematics210 New YorkDover.01AxxHistory of mathematics and mathematicians [MSC 2020]MFSUNC019751USNew YorkSUNL000011Klein, JacobSUNV04335448243DoverSUNV000279650ITSOL20200720RICAhttps://books.google.it/books?id=g1FOGSKSo4cC&pg=PA26&dq=9780486272894&hl=it&sa=X&ved=0ahUKEwjU64i0naXaAhWESBQKHQHGC24QuwUILTAA#v=onepage&q=9780486272894&f=falsePreviewSUN0054852UFFICIO DI BIBLIOTECA DEL DIPARTIMENTO DI MATEMATICA E FISICA08CONS 01-XX 2207 08 616 I a 20061025 UFFICIO DI BIBLIOTECA DEL DIPARTIMENTO DI MATEMATICA E FISICA08PREST 01-XX 2207 08 3385 I b 20061025 Greek mathematical thought and the origin of algebra921953UNICAMPANIA00908nam--2200325---450 99000053237020331620210616112627.00053237USA010053237(ALEPH)000053237USA01005323720010629d1988----km-y0itay0103----baitaIT||||||||001yySud oggicom'è cambiata e può cambiare la questione meridionaleMimmo Della CorteNapoliDe Dominicis1988246 p.21 cm... Oggi12001... Oggi12Questione meridionaleSaggi945.709DELLA CORTE,Mimmo546150ITsalbcISBD990000532370203316X.3.B. 2222 (III E COLL. 165/1)99874 L.M.III E COLL.BKUMASud oggi886455UNISA05047nam 22005895 450 991096408900332120250813214845.01-4612-4418-810.1007/978-1-4612-4418-9(CKB)3400000000090833(SSID)ssj0001298329(PQKBManifestationID)11686514(PQKBTitleCode)TC0001298329(PQKBWorkID)11242049(PQKB)11453617(DE-He213)978-1-4612-4418-9(MiAaPQ)EBC3076571(PPN)238060519(EXLCZ)99340000000009083320121227d1992 u| 0engurnn#008mamaatxtccrRings and Categories of Modules /by Frank W. Anderson, Kent R. Fuller2nd ed. 1992.New York, NY :Springer New York :Imprint: Springer,1992.1 online resource (X, 378 p.)Graduate Texts in Mathematics,2197-5612 ;13Bibliographic Level Mode of Issuance: Monograph0-387-97845-3 1-4612-8763-4 Includes bibliographical references and index.§0. Preliminaries -- 1: Rings, Modules and Homomorphisms -- §1. Review of Rings and their Homomorphisms -- §2. Modules and Submodules -- §3. Homomorphisms of Modules -- §4. Categories of Modules; Endomorphism Rings -- 2: Direct Sums and Products -- §5. Direct Summands -- §6. Direct Sums and Products of Modules -- §7. Decomposition of Rings -- §8. Generating and Cogenerating -- 3: Finiteness Conditions for Modules -- §9. Semisimple Modules—The Sode and the Radical -- §10. Finitely Generated and Finitely Cogenerated Modules—Chain Conditions -- §11. Modules with Composition Series -- §12. Indecomposable Decompositions of Modules -- 4: Classical Ring-Structure Theorems -- §13. Semisimple Rings -- §14. The Density Theorem -- §15. The Radical of a Ring—Local Rings and Artinian Rings -- 5: Functors Between Module Categories -- §16. The Horn Functors and Exactness—Projectivity and Injectivity -- §17. Projective Modules and Generators -- §18. Injective Modules and Cogenerators -- §19. The Tensor Functors and Flat Modules -- §20. Natural Transformations -- 6: Equivalence and Duality for Module Categories -- §21. Equivalent Rings -- §22. The Morita Characterizations of Equivalence -- §23. Dualities -- §24. Morita Dualities -- 7: Injective Modules, Projective Modules, and Their Decompositions -- §25. Injective Modules and Noetherian Rings—The Faith-Walker Theorems -- §26. Direct Sums of Countably Generated Modules—With Local Endomorphism Rings -- §27. Semiperfect Rings -- §28. Perfect Rings -- §29. Modules with Perfect Endomorphism Rings -- 8: Classical Artinian Rings -- §30. Artinian Rings with Duality -- §31. Injective Projective Modules -- §32. Serial Rings -- References.This book is intended to provide a reasonably self-contained account of a major portion of the general theory of rings and modules suitable as a text for introductory and more advanced graduate courses. We assume the famil­ iarity with rings usually acquired in standard undergraduate algebra courses. Our general approach is categorical rather than arithmetical. The continuing theme of the text is the study of the relationship between the one-sided ideal structure that a ring may possess and the behavior of its categories of modules. Following a brief outline of set-theoretic and categorical foundations, the text begins with the basic definitions and properties of rings, modules and homomorphisms and ranges through comprehensive treatments of direct sums, finiteness conditions, the Wedderburn-Artin Theorem, the Jacobson radical, the hom and tensor functions, Morita equivalence and duality, de­ composition theory of injective and projective modules, and semi perfect and perfect rings. In this second edition we have included a chapter containing many of the classical results on artinian rings that have hdped to form the foundation for much of the contemporary research on the representation theory of artinian rings and finite dimensional algebras. Both to illustrate the text and to extend it we have included a substantial number of exercises covering a wide spectrum of difficulty. There are, of course" many important areas of ring and module theory that the text does not touch upon.Graduate Texts in Mathematics,2197-5612 ;13AlgebraAlgebraAlgebra.Algebra.51216-02mscAnderson Frank Wauthttp://id.loc.gov/vocabulary/relators/aut536705Fuller Kent Rauthttp://id.loc.gov/vocabulary/relators/autMiAaPQMiAaPQMiAaPQBOOK9910964089003321Rings and categories of modules924541UNINA