RINGS WHOSE CYCLIC MODULES ARE DIRECT SUMS OF EXTENDING MODULES

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dc.authoridEr, Noyan/0000-0002-9225-3587
dc.authoridAydogdu, Pinar/0000-0002-2148-2980
dc.contributor.authorAydogdu, Pinar
dc.contributor.authorEr, Noyan
dc.contributor.authorErtas, Nil Orhan
dc.date.accessioned2024-09-29T16:00:57Z
dc.date.available2024-09-29T16:00:57Z
dc.date.issued2012
dc.departmentKarabük Üniversitesien_US
dc.description.abstractDedekind domains, Artinian serial rings and right uniserial rings share the following property: Every cyclic right module is a direct sum of uniform modules. We first prove the following improvement of the well-known Osofsky-Smith theorem: Acyclic module with every cyclic subfactor a direct sum of extending modules has finite Goldie dimension. So, rings with the above-mentioned property are precisely rings of the title. Furthermore, a ring R is right q.f.d. (cyclics with finite Goldie dimension) if proper cyclic (not congruent to R-R) right R-modules are direct sums of extending modules. R is right serial with all prime ideals maximal and boolean AND(n is an element of N)J(n) = J(m) for some m is an element of N if cyclic right R-modules are direct sums of quasi-injective modules. A right non-singular ring with the latter property is right Artinian. Thus, hereditary Artinian serial rings are precisely one-sided non-singular rings whose right and left cyclic modules are direct sums of quasi-injectives.en_US
dc.description.sponsorshipTUBITAK (The Scientific and Technological Research Council of Turkey)en_US
dc.description.sponsorshipThe first and the third authors acknowledge the support they received from TUBITAK (The Scientific and Technological Research Council of Turkey) for their visit to the Ohio University Center of Ring Theory and its Applications. Part of this work was done during that visit. All authors would like to thank the Center and its members for the warm hospitality they received. Finally, we are greatly indebted to the referee for his/her careful reading of the manuscript and for making very helpful suggestions that have improved the paper.en_US
dc.identifier.doi10.1017/S0017089512000183
dc.identifier.endpage617en_US
dc.identifier.issn0017-0895
dc.identifier.issn1469-509X
dc.identifier.issue3en_US
dc.identifier.scopus2-s2.0-84864543879en_US
dc.identifier.scopusqualityQ2en_US
dc.identifier.startpage605en_US
dc.identifier.urihttps://doi.org/10.1017/S0017089512000183
dc.identifier.urihttps://hdl.handle.net/20.500.14619/5453
dc.identifier.volume54en_US
dc.identifier.wosWOS:000307171200010en_US
dc.identifier.wosqualityQ3en_US
dc.indekslendigikaynakWeb of Scienceen_US
dc.indekslendigikaynakScopusen_US
dc.language.isoenen_US
dc.publisherCambridge Univ Pressen_US
dc.relation.ispartofGlasgow Mathematical Journalen_US
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanıen_US
dc.rightsinfo:eu-repo/semantics/openAccessen_US
dc.titleRINGS WHOSE CYCLIC MODULES ARE DIRECT SUMS OF EXTENDING MODULESen_US
dc.typeArticleen_US

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