All listings for this product
Best-selling in Textbooks
Save on Textbooks
- AU $27.54Trending at AU $43.90
- AU $80.99Trending at AU $87.85
- AU $72.90Trending at AU $77.47
- AU $71.88Trending at AU $73.18
- AU $82.89Trending at AU $85.35
- AU $72.90Trending at AU $79.34
- AU $34.77Trending at AU $42.60
About this product
- DescriptionThisexpositorymographwaswrittenforthreereasons. Firstly,wewantedto present the solution to a problem posed by Wolfgang Krull in 1932 [Krull 32]. He asked whether what we w 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 phemen in the history of Krull-Schmidt type theorems. Essentially, the Krull-Schmidt Theorem holds for some classes of modules and t for others. When it does hold, any two indecomposable decompositions are uniquely determined up to a permutation, and when it does t hold for a class of modules, this is proved via an example. For serial modules the Krull-Schmidt Theorem does t hold, but any two indecomposable decompositions are uniquely determined up to two permutations. We wanted to present such a phemen to a wider ma- ematical audience.
- Author BiographyAlberto Facchini is a Professor of Mathematics at the University of Padua.
- Author(s)Alberto Facchini
- PublisherSpringer Basel
- Date of Publication04/02/2012
- Series TitleModern Birkhauser Classics
- Country of PublicationSwitzerland
- ImprintSpringer Basel
- Content Notebiography
- Weight462 g
- Width156 mm
- Height234 mm
- Spine15 mm
- Format DetailsTrade paperback (US)
- Edition Statement1998
This item doesn't belong on this page.
Thanks, we'll look into this.