FI- and OI-modules with varying coefficients
DC Element | Wert | Sprache |
---|---|---|
dc.contributor.author | Nagel, Uwe | |
dc.contributor.author | Roemer, Tim | |
dc.date.accessioned | 2021-12-23T16:11:22Z | - |
dc.date.available | 2021-12-23T16:11:22Z | - |
dc.date.issued | 2019 | |
dc.identifier.issn | 00218693 | |
dc.identifier.uri | https://osnascholar.ub.uni-osnabrueck.de/handle/unios/9667 | - |
dc.description.abstract | We introduce FI-algebras over a commutative ring K and the category of FI-modules over an FI-algebra. Such a module may be considered as a family of invariant modules over compatible varying K-algebras. FI-modules over K correspond to the well studied constant coefficient case where every algebra equals K. We show that a finitely generated FI-module over a noetherian polynomial FI-algebra is a noetherian module. This is established by introducing OI-modules. We prove that every submodule of a finitely generated free OI-module over a noetherian polynomial Of-algebra has a finite Grobner basis. Applying our noetherianity results to a family of free resolutions, finite generation translates into stabilization of syzygies in any fixed homological degree. In particular, in the graded case this gives uniformity results on degrees of minimal syzygies. (C) 2019 Elsevier Inc. All rights reserved. | |
dc.description.sponsorship | Simons Foundation [317096]; The first author was partially supported by Simons Foundation grant #317096. He also is grateful to Daniel Errnan and Greg Smith for organizing a very inspiring April 2016 Banff workshop on Free Resolutions, Representations, and Asymptotic Algebra. Both authors thank the referee for helpful comments. | |
dc.language.iso | en | |
dc.publisher | ACADEMIC PRESS INC ELSEVIER SCIENCE | |
dc.relation.ispartof | JOURNAL OF ALGEBRA | |
dc.subject | Category | |
dc.subject | Functor | |
dc.subject | Grobner basis | |
dc.subject | IDEALS | |
dc.subject | Mathematics | |
dc.subject | Noetherian | |
dc.subject | NOETHERIANITY | |
dc.subject | RANK SYMMETRIC TENSORS | |
dc.subject | STABILITY | |
dc.subject | SYZYGIES | |
dc.subject | Syzygy | |
dc.title | FI- and OI-modules with varying coefficients | |
dc.type | journal article | |
dc.identifier.doi | 10.1016/j.jalgebra.2019.06.029 | |
dc.identifier.isi | ISI:000480373700008 | |
dc.description.volume | 535 | |
dc.description.startpage | 286 | |
dc.description.endpage | 322 | |
dc.contributor.orcid | 0000-0003-3459-5148 | |
dc.identifier.eissn | 1090266X | |
dc.publisher.place | 525 B ST, STE 1900, SAN DIEGO, CA 92101-4495 USA | |
dcterms.isPartOf.abbreviation | J. Algebra | |
dcterms.oaStatus | Green Submitted | |
crisitem.author.dept | FB 06 - Mathematik/Informatik | - |
crisitem.author.deptid | fb06 | - |
crisitem.author.parentorg | Universität Osnabrück | - |
crisitem.author.netid | RoTi119 | - |
Seitenaufrufe
2
Letzte Woche
0
0
Letzter Monat
2
2
geprüft am 07.06.2024