On the relation between length functions and exact Sylvester rank functions
Inspired by the work of Crawley-Boevey on additive functions in locally finitely presented Grothendieck categories, we describe a natural way to extend a given exact Sylvester rank function on the category of finitely presented left modules over a given ring R, to the category of all left R-modules.
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| Format: | Article |
| Language: | English |
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De Gruyter
2019-12-01
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| Series: | Topological Algebra and its Applications |
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| Online Access: | https://doi.org/10.1515/taa-2019-0006 |
| _version_ | 1818739650504687616 |
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| author | Virili Simone |
| author_facet | Virili Simone |
| author_sort | Virili Simone |
| collection | DOAJ |
| description | Inspired by the work of Crawley-Boevey on additive functions in locally finitely presented Grothendieck categories, we describe a natural way to extend a given exact Sylvester rank function on the category of finitely presented left modules over a given ring R, to the category of all left R-modules. |
| first_indexed | 2024-12-18T01:28:12Z |
| format | Article |
| id | doaj.art-5bcfa084ae0742a3bbaaeb604cfaf7d7 |
| institution | Directory Open Access Journal |
| issn | 2299-3231 |
| language | English |
| last_indexed | 2024-12-18T01:28:12Z |
| publishDate | 2019-12-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Topological Algebra and its Applications |
| spelling | doaj.art-5bcfa084ae0742a3bbaaeb604cfaf7d72022-12-21T21:25:39ZengDe GruyterTopological Algebra and its Applications2299-32312019-12-0171697410.1515/taa-2019-0006taa-2019-0006On the relation between length functions and exact Sylvester rank functionsVirili Simone0Universidad de Murcia Murcia, MurciaSpainInspired by the work of Crawley-Boevey on additive functions in locally finitely presented Grothendieck categories, we describe a natural way to extend a given exact Sylvester rank function on the category of finitely presented left modules over a given ring R, to the category of all left R-modules.https://doi.org/10.1515/taa-2019-0006sylvester rank functionlength functionadditivityextension of invariantsmatrix rank functionprimary 16d10secondary 16e50, 16e20 |
| spellingShingle | Virili Simone On the relation between length functions and exact Sylvester rank functions Topological Algebra and its Applications sylvester rank function length function additivity extension of invariants matrix rank function primary 16d10 secondary 16e50, 16e20 |
| title | On the relation between length functions and exact Sylvester rank functions |
| title_full | On the relation between length functions and exact Sylvester rank functions |
| title_fullStr | On the relation between length functions and exact Sylvester rank functions |
| title_full_unstemmed | On the relation between length functions and exact Sylvester rank functions |
| title_short | On the relation between length functions and exact Sylvester rank functions |
| title_sort | on the relation between length functions and exact sylvester rank functions |
| topic | sylvester rank function length function additivity extension of invariants matrix rank function primary 16d10 secondary 16e50, 16e20 |
| url | https://doi.org/10.1515/taa-2019-0006 |
| work_keys_str_mv | AT virilisimone ontherelationbetweenlengthfunctionsandexactsylvesterrankfunctions |