Module Theory - Endomorphism rings and direct sum decompositions in some classes of modules (Paperback, 1998)

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.

General

Imprint:	Birkhauser Verlag AG
Country of origin:	Switzerland
Series:	Modern Birkhauser Classics
Release date:	February 2012
First published:	1998
Authors:	Alberto Facchini
Dimensions:	235 x 155 x 17mm (L x W x T)
Format:	Paperback
Pages:	285
Edition:	1998
ISBN-13:	978-3-03-480302-1
Categories:	Books > Science & Mathematics > Mathematics > Algebra > General Promotions
LSN:	3-03-480302-8
Barcode:	9783034803021

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