Module Theory: Endomorphism rings and direct sum decompositions in some classes of modules
Gespeichert in:
| Beteilige Person: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | Englisch |
| Veröffentlicht: |
Basel
Birkhäuser Basel
1998
|
| Schriftenreihe: | Progress in Mathematics
167 |
| Schlagwörter: | |
| Links: | https://doi.org/10.1007/978-3-0348-8774-8 |
| Beschreibung: | This expository monograph was written for three reasons. Firstly, we wanted to present the solution to a problem posed by Wolfgang Krull in 1932 [Krull 32]. He asked whether what we now call the "Krull-Schmidt Theorem" holds for artinian modules. The problem remained open for 63 years: its solution, a negative 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 Warfield in 1975 [Warfield 75]. He proved that every finitely presented module over a serial ring is a direct sum of uniserial modules, and asked if such a decomposition was unique. In other words, Warfield 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 solution to Warfield'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 mathematical audience |
| Umfang: | 1 Online-Ressource (XIII, 288 p) |
| ISBN: | 9783034887748 9783034897693 |
| ISSN: | 0743-1643 |
| DOI: | 10.1007/978-3-0348-8774-8 |
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| 245 | 1 | 0 | |a Module Theory |b Endomorphism rings and direct sum decompositions in some classes of modules |c by Alberto Facchini |
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Datensatz im Suchindex
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| format | Electronic eBook |
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| id | DE-604.BV042422228 |
| illustrated | Not Illustrated |
| indexdate | 2024-12-20T17:10:46Z |
| institution | BVB |
| isbn | 9783034887748 9783034897693 |
| issn | 0743-1643 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027857645 |
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| physical | 1 Online-Ressource (XIII, 288 p) |
| psigel | ZDB-2-SMA ZDB-2-BAE ZDB-2-SMA_Archive |
| publishDate | 1998 |
| publishDateSearch | 1998 |
| publishDateSort | 1998 |
| publisher | Birkhäuser Basel |
| record_format | marc |
| series | Progress in Mathematics |
| series2 | Progress in Mathematics |
| spellingShingle | Facchini, Alberto Module Theory Endomorphism rings and direct sum decompositions in some classes of modules Progress in Mathematics Mathematics Algebra Mathematik Modultheorie (DE-588)4170336-4 gnd Ringtheorie (DE-588)4126571-3 gnd |
| subject_GND | (DE-588)4170336-4 (DE-588)4126571-3 |
| title | Module Theory Endomorphism rings and direct sum decompositions in some classes of modules |
| title_auth | Module Theory Endomorphism rings and direct sum decompositions in some classes of modules |
| title_exact_search | Module Theory Endomorphism rings and direct sum decompositions in some classes of modules |
| title_full | Module Theory Endomorphism rings and direct sum decompositions in some classes of modules by Alberto Facchini |
| title_fullStr | Module Theory Endomorphism rings and direct sum decompositions in some classes of modules by Alberto Facchini |
| title_full_unstemmed | Module Theory Endomorphism rings and direct sum decompositions in some classes of modules by Alberto Facchini |
| title_short | Module Theory |
| title_sort | module theory endomorphism rings and direct sum decompositions in some classes of modules |
| title_sub | Endomorphism rings and direct sum decompositions in some classes of modules |
| topic | Mathematics Algebra Mathematik Modultheorie (DE-588)4170336-4 gnd Ringtheorie (DE-588)4126571-3 gnd |
| topic_facet | Mathematics Algebra Mathematik Modultheorie Ringtheorie |
| url | https://doi.org/10.1007/978-3-0348-8774-8 |
| volume_link | (DE-604)BV000004120 |
| work_keys_str_mv | AT facchinialberto moduletheoryendomorphismringsanddirectsumdecompositionsinsomeclassesofmodules |