FI- and OI-modules with varying coefficients

DC FieldValueLanguage
dc.contributor.authorNagel, Uwe
dc.contributor.authorRoemer, Tim
dc.date.accessioned2021-12-23T16:11:22Z-
dc.date.available2021-12-23T16:11:22Z-
dc.date.issued2019
dc.identifier.issn00218693
dc.identifier.urihttps://osnascholar.ub.uni-osnabrueck.de/handle/unios/9667-
dc.description.abstractWe 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.sponsorshipSimons 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.isoen
dc.publisherACADEMIC PRESS INC ELSEVIER SCIENCE
dc.relation.ispartofJOURNAL OF ALGEBRA
dc.subjectCategory
dc.subjectFunctor
dc.subjectGrobner basis
dc.subjectIDEALS
dc.subjectMathematics
dc.subjectNoetherian
dc.subjectNOETHERIANITY
dc.subjectRANK SYMMETRIC TENSORS
dc.subjectSTABILITY
dc.subjectSYZYGIES
dc.subjectSyzygy
dc.titleFI- and OI-modules with varying coefficients
dc.typejournal article
dc.identifier.doi10.1016/j.jalgebra.2019.06.029
dc.identifier.isiISI:000480373700008
dc.description.volume535
dc.description.startpage286
dc.description.endpage322
dc.contributor.orcid0000-0003-3459-5148
dc.identifier.eissn1090266X
dc.publisher.place525 B ST, STE 1900, SAN DIEGO, CA 92101-4495 USA
dcterms.isPartOf.abbreviationJ. Algebra
dcterms.oaStatusGreen Submitted
crisitem.author.deptFB 06 - Mathematik/Informatik-
crisitem.author.deptidfb06-
crisitem.author.parentorgUniversität Osnabrück-
crisitem.author.netidRoTi119-
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