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

Alberto Facchini

ISBN 10: 3034803028 / ISBN 13: 9783034803021

Editore: Springer Basel, 2012

Riguardo questo articolo

Module Theory | Endomorphism rings and direct sum decompositions in some classes of modules | Alberto Facchini | Taschenbuch | xiii | Englisch | 2012 | Springer Basel | EAN 9783034803021 | Verantwortliche Person für die EU: Springer Basel AG in Springer Science + Business Media, Heidelberger Platz 3, 14197 Berlin, juergen[dot]hartmann[at]springer[dot]com | Anbieter: preigu.

Codice articolo 106720343

Dati bibliografici

• Titolo: Module Theory | Endomorphism rings and direct sum decompositions in some classes of modules
• Editore: Springer Basel
• Data di pubblicazione: 2012
• Lingua: Inglese
• ISBN 10: 3034803028
• ISBN 13: 9783034803021
• Rilegatura: Taschenbuch
• Condizione: Neu
• Dimensioni: 235 L x 155 A x 17 P (millimetri) 235 millimetri di larghezza per 155 millimetri di altezza per 17 millimetri di profondità
• Peso: 458 grammi
• Cataloghi dei venditori:
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Descrizione articolo

Riassunto

Thisexpositorymonographwaswrittenforthreereasons. Firstly,wewantedto present the solution to a problem posed by Wolfgang Krull in 1932 [Krull 32]. He asked whether what we now call the “Krull-SchmidtTheorem” holds for - tinianmodules. Theproblemremainedopenfor63years:itssolution,anegative answer to Krull’s question, was published only in 1995 (see [Facchini, Herbera, Levy and Vamos]). ´ Secondly, we wanted to present the answer to a question posed by War?eld in 1975 [War?eld 75]. He proved that every ?nitely p- sented module over a serial ring is a direct sum of uniserial modules, and asked if such a decomposition was unique. In other words, War?eld asked whether the “Krull-Schmidt Theorem” holds for serial modules. The solution to this problem, a negative answer again, appeared in [Facchini 96]. Thirdly, the - lution to War?eld’s problem shows interesting behavior, a rare phenomenon in the history of Krull-Schmidt type theorems. Essentially, the Krull-Schmidt Theorem holds for some classes of modules and not for others. When it does hold, any two indecomposable decompositions are uniquely determined up to a permutation, and when it does not hold for a class of modules, this is proved via an example. For serial modules the Krull-Schmidt Theorem does not hold, but any two indecomposable decompositions are uniquely determined up to two permutations. We wanted to present such a phenomenon to a wider ma- ematical audience.

Informazioni sull?autore

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