| Title:
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MODULE THEORY
ENDOMORPHISM RINGS AND DIRECT SUM DECOMPOSITIONS IN SOME CLASSES OF MODULES |
| By: |
Alberto Facchini |
| Format: |
Paperback |
| List price:
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£64.99 |
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£56.87 |
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£8.12 |
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| ISBN 10: |
3034803028 |
| ISBN 13: |
9783034803021 |
| Availability: |
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| Publisher: |
SPRINGER BASEL |
| Pub. date: |
4 February, 2012 |
| Edition: |
1998 |
| Series: |
Modern Birkhauser Classics |
| Pages: |
298 |
| Description: |
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. |
| Synopsis: |
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. |
| Illustrations: |
biography |
| Publication: |
Switzerland |
| Imprint: |
Springer Basel |
| Returns: |
Returnable |
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