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

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

Autor Alberto Facchini
en Limba Engleză Paperback – 5 feb 2012
This book presents topics in module theory and ring theory: some, such as Goldie dimension and semiperfect rings are now considered classical and others more specialized, such as dual Goldie dimension, semilocal endomorphism rings, serial rings and modules.
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Paperback (1) 47313 lei  6-8 săpt.
  Springer – 5 feb 2012 47313 lei  6-8 săpt.
Hardback (1) 61312 lei  6-8 săpt.
  Birkhäuser Basel – 16 iun 1998 61312 lei  6-8 săpt.

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Specificații

ISBN-13: 9783034803021
ISBN-10: 3034803028
Pagini: 299
Ilustrații: XIII, 285 p.
Dimensiuni: 155 x 235 x 20 mm
Greutate: 0.42 kg
Ediția:1998
Editura: Springer
Colecția Birkhäuser
Seria Modern Birkhäuser Classics

Locul publicării:Basel, Switzerland

Public țintă

Research

Cuprins

Basic Concepts.- The Krull-Schmidt-Remak-Azumaya Theorem.- Semiperfect Rings.- Semilocal Rings.- Serial Rings.- Quotient Rings.- Krull Dimension and Serial Rings.- Krull-Schmidt Fails for Finitely Generated Modules and Artinian Modules.- Biuniform Modules.- ?-pure-injective Modules and Artinian Modules.- Open Problems.

Notă biografică

Alberto Facchini is a Professor of Mathematics at the University of Padua.

Textul de pe ultima copertă

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.
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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)

Caracteristici

Adds to the list of fundamental books on rings and modules Develops the necessary background in a logical way Joyful reading for algebraists ? Includes supplementary material: sn.pub/extras

Recenzii

"Written in an attractive and fresh mathematical style. Each topic is arranged well and lucidly. The author has made important contributions to the study of direct sum decompositions and many of the main results in this book include his own work."
--EMS Newsletter