Module Theory : Endomorphism rings and direct sum decompositions in some classes of modules

Lingua: inglese

Editore: Birkhäuser, 2012

3034803028 / 9783034803021

Da: AHA-BUCH GmbH, Einbeck, GermaniaAHA-BUCH GmbH

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Venditore AbeBooks dal 14 agosto 2006

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Druck auf Anfrage Neuware - Printed after ordering - The purpose of this expository monograph is three-fold. First, the solution of a problem posed by Wolfgang Krull in 1932 is presented. He asked whether what is now called the 'Krull-Schmidt Theorem' holds for artinian modules. A negative answer was published only in 1995 by Facchini, Herbera, Levy and Vámos. Second, the answer to a question posed by Warfield in 1975, namely, whether the Krull-Schmidt-Theorem holds for serial modules, is described. Facchini published a negative answer in 1996. The solution to the Warfield problem shows an interesting behavior; in fact, it is a phenomena so rare in the history of Krull-Schmidt type theorems that its presentation to a wider mathematical audience provides the third incentive for this monograph. Briefly, the Krull-Schmidt-Theorem holds for some, not all, classes of modules. When it does hold, any two indecomposable decompositions are uniquely determined up to one permutation. For serial modules the theorem does not hold, but any two indecomposable decompositions are uniquely determined up to two permutations.Apart from these issues, the book addresses various topics in module theory and ring theory, some now considered classical (such as Goldie dimension, semiperfect rings, Krull dimension, rings of quotients, and their applications) and others more specialized (such as dual Goldie dimension, semilocal endomorphism rings, serial rings and modules, exchange property, (sigma)-pure-injective modules). Open problems conclude the work.--------Besides its research value, this book is a considerable addition to the list of fundamental books in rings and modules. It is written carefully with necessary backgrounds developed in a logical way. There are many fundamental points worked out in the book. All these make the book an excellent contribution to the development of module and ring theory, and a source of reference. Algebraists will certainly enjoy themselves in reading thisbook.(Zentralblatt MATH)This excellent book on module and ring theory (.) contains three kind of topics: classical topics, (.) specialized topics, (.) the solutions to two famous problems, together with the presentation of a rare phenomenon.(Mathematica).…

Codice articolo 9783034803021

Titolo
Module Theory : Endomorphism rings and direct sum decompositions in some classes of modules
Autore
Alberto Facchini
Editore
Birkhäuser
Anno di pubblicazione
2012
Condizione
Neu
Rilegatura
Taschenbuch
Lingua
inglese
ISBN 10
3034803028
ISBN 13
9783034803021
Peso dell'articolo
458 grammi
Dimensioni
235x155x17 mm

AHA-BUCH GmbH

Einbeck, Germania

Venditore con 5 stelle

Venditore AbeBooks dal 14 agosto 2006

Tariffe di spedizione da Germania a U.S.A.

ArticoloDa 7 a 10 giorni lavorativiDa 5 a 7 giorni lavorativi
Primo articoloEUR 35,00EUR 45,00
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