Categories of lattices, and their global structure in terms of almost split sequences
A major part of Iyama’s characterization of
 Auslander-Reiten quivers of representation-finite orders Λ consists
 of an induction via rejective subcategories of Λ-lattices, which
 amounts to a resolution of Λ as an isolated singularity. Despite
 of its useful applicat...
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| Published in: | Algebra and Discrete Mathematics |
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| Date: | 2004 |
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| Format: | Article |
| Language: | English |
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Інститут прикладної математики і механіки НАН України
2004
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/155952 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Categories of lattices, and their global structure in terms of almost split sequences / W. Rump // Algebra and Discrete Mathematics. — 2004. — Vol. 3, № 1. — С. 87–111. — Бібліогр.: 30 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862737173142306816 |
|---|---|
| author | Rump, W. |
| author_facet | Rump, W. |
| citation_txt | Categories of lattices, and their global structure in terms of almost split sequences / W. Rump // Algebra and Discrete Mathematics. — 2004. — Vol. 3, № 1. — С. 87–111. — Бібліогр.: 30 назв. — англ. |
| collection | DSpace DC |
| container_title | Algebra and Discrete Mathematics |
| description | A major part of Iyama’s characterization of
Auslander-Reiten quivers of representation-finite orders Λ consists
of an induction via rejective subcategories of Λ-lattices, which
amounts to a resolution of Λ as an isolated singularity. Despite
of its useful applications (proof of Solomon’s second conjecture
and the finiteness of representation dimension of any artinian algebra), rejective induction cannot be generalized to higher dimensional Cohen-Macaulay orders Λ. Our previous characterization
of finite Auslander-Reiten quivers of Λ in terms of additive functions [22] was proved by means of L-functors, but we still had to
rely on rejective induction. In the present article, this dependence
will be eliminated.
|
| first_indexed | 2025-12-07T19:57:25Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-155952 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1726-3255 |
| language | English |
| last_indexed | 2025-12-07T19:57:25Z |
| publishDate | 2004 |
| publisher | Інститут прикладної математики і механіки НАН України |
| record_format | dspace |
| spelling | Rump, W. 2019-06-17T15:48:26Z 2019-06-17T15:48:26Z 2004 Categories of lattices, and their global structure in terms of almost split sequences / W. Rump // Algebra and Discrete Mathematics. — 2004. — Vol. 3, № 1. — С. 87–111. — Бібліогр.: 30 назв. — англ. 1726-3255 2000 Mathematics Subject Classification: 16G30, 16G70, 18E10; 16G60. https://nasplib.isofts.kiev.ua/handle/123456789/155952 A major part of Iyama’s characterization of
 Auslander-Reiten quivers of representation-finite orders Λ consists
 of an induction via rejective subcategories of Λ-lattices, which
 amounts to a resolution of Λ as an isolated singularity. Despite
 of its useful applications (proof of Solomon’s second conjecture
 and the finiteness of representation dimension of any artinian algebra), rejective induction cannot be generalized to higher dimensional Cohen-Macaulay orders Λ. Our previous characterization
 of finite Auslander-Reiten quivers of Λ in terms of additive functions [22] was proved by means of L-functors, but we still had to
 rely on rejective induction. In the present article, this dependence
 will be eliminated. en Інститут прикладної математики і механіки НАН України Algebra and Discrete Mathematics Categories of lattices, and their global structure in terms of almost split sequences Article published earlier |
| spellingShingle | Categories of lattices, and their global structure in terms of almost split sequences Rump, W. |
| title | Categories of lattices, and their global structure in terms of almost split sequences |
| title_full | Categories of lattices, and their global structure in terms of almost split sequences |
| title_fullStr | Categories of lattices, and their global structure in terms of almost split sequences |
| title_full_unstemmed | Categories of lattices, and their global structure in terms of almost split sequences |
| title_short | Categories of lattices, and their global structure in terms of almost split sequences |
| title_sort | categories of lattices, and their global structure in terms of almost split sequences |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/155952 |
| work_keys_str_mv | AT rumpw categoriesoflatticesandtheirglobalstructureintermsofalmostsplitsequences |