Please use this identifier to cite or link to this item: https://hdl.handle.net/11147/15386
Full metadata record
DC FieldValueLanguage
dc.contributor.authorBuyukasik, Engin-
dc.contributor.authorDemir, Ozlem Irmak-
dc.date.accessioned2025-02-25T20:00:53Z-
dc.date.available2025-02-25T20:00:53Z-
dc.date.issued2025-
dc.identifier.issn0219-4988-
dc.identifier.issn1793-6829-
dc.identifier.urihttps://doi.org/10.1142/S0219498826501021-
dc.identifier.urihttps://hdl.handle.net/11147/15386-
dc.description.abstractIn this paper, we call a right module M (strongly) virtually regular if every (finitely generated) cyclic submodule of M is isomorphic to a direct summand of M. M is said to be completely virtually regular if every submodule of M is virtually regular. In this paper, characterizations and some closure properties of the aforementioned modules are given. Several structure results are obtained over commutative rings. In particular, the structures of finitely presented (strongly) virtually regular modules and completely virtually regular modules are fully determined over valuation domains. Namely, for a valuation domain R with the unique nonzero maximal ideal P, we show that finitely presented (strongly) virtually regular modules are free if and only if P is not principal; and that P = Rp is principal if and only if finitely presented virtually regular modules are of the form R-n circle plus (R/Rp)(n)(1) circle plus (R/Rp(2))(n)(2) circle plus center dot center dot center dot circle plus (R/Rp(k))(n)(k) for nonnegative integers n, k, n(1), n(2),...,n(k). Similarly, we prove that P = Rp is principal if and only if finitely presented strongly virtually regular modules are of the form R-n circle plus (R/Rp)(m), where m,n are nonnegative integers. We also obtain that, R admits a nonzero finitely presented completely virtually regular module M if and only if P = Rp is principal. Moreover, for a finitely presented R-module M, we prove that: (i) if R is not a DVR, then M is completely virtually regular if and only if M congruent to( R/Rp)(m); and (ii) if R is a DVR, then M is completely virtually regular if and only if M congruent to R-n circle plus ( R/Rp)(m). Finally, we obtain a characterization of finitely generated virtually regular modules over the ring of integers.en_US
dc.language.isoenen_US
dc.publisherWorld Scientific Publ Co Pte Ltden_US
dc.rightsinfo:eu-repo/semantics/openAccessen_US
dc.subjectRegular Ringsen_US
dc.subjectStrongly Regular Modulesen_US
dc.subjectVirtually Regular Modulesen_US
dc.subjectValuation Domainsen_US
dc.titleVirtually Regular Modulesen_US
dc.typeArticleen_US
dc.departmentİzmir Institute of Technologyen_US
dc.identifier.wosWOS:001407195900001-
dc.identifier.scopus2-s2.0-85216374720-
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanıen_US
dc.identifier.doi10.1142/S0219498826501021-
dc.authorscopusid6504488611-
dc.authorscopusid57219738612-
dc.identifier.wosqualityQ3-
dc.identifier.scopusqualityQ3-
dc.description.woscitationindexScience Citation Index Expanded-
item.cerifentitytypePublications-
item.openairetypeArticle-
item.languageiso639-1en-
item.fulltextNo Fulltext-
item.openairecristypehttp://purl.org/coar/resource_type/c_18cf-
item.grantfulltextnone-
crisitem.author.dept04.02. Department of Mathematics-
Appears in Collections:Scopus İndeksli Yayınlar Koleksiyonu / Scopus Indexed Publications Collection
WoS İndeksli Yayınlar Koleksiyonu / WoS Indexed Publications Collection
Show simple item record



CORE Recommender

Page view(s)

12
checked on Mar 3, 2025

Google ScholarTM

Check




Altmetric


Items in GCRIS Repository are protected by copyright, with all rights reserved, unless otherwise indicated.