Rings whose modules have maximal or minimal projectivity domain

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dc.authoridLopez-Permouth, Sergio/0000-0002-7376-2167
dc.contributor.authorHolston, Chris
dc.contributor.authorLopez-Permouth, Sergio R.
dc.contributor.authorErtas, Nil Orhan
dc.date.accessioned2024-09-29T15:57:46Z
dc.date.available2024-09-29T15:57:46Z
dc.date.issued2012
dc.departmentKarabük Üniversitesien_US
dc.description.abstractUsing the notion of relative projectivity, projective modules may be thought of as being those which are projective relative to all others. In contrast, a module M is said to be projectively poor if it is projective relative only to semisimple modules. We prove that all rings have projectively poor modules. In fact, every ring even has a semisimple projectively poor module. Properties of projectively poor modules are studied and particular emphasis is given to the study of modules over PCI domains; we note that over such domains when all right ideals are principal most modules seem to be either projective or projectively poor. We consider rings over which modules are either projective or projectively poor and call them rings without a p-middle class. We show that a QF ring R with homogeneous right socle and J(R)(2) = 0 has no right p-middle class. As we analyze the structure of rings with no right p-middle class, among other results, we show that any such ring is the ring direct sum of a semisimple artinian ring and a ring K which is either zero or an indecomposable ring such that either (i) K is a semiprimary right SI-ring with J(K) not equal 0, or (ii) K is a semiprimary ring with Soc(K-K) = Z(r)(K) = J(K) not equal 0, or (iii) K is a prime ring with Soc(K-K) = 0, and either f (K) = 0 or (K)J(K) and J(K)(K) are infinitely generated, or (iv) K is a prime right SI-ring with infinitely generated right socle. (C) 2011 Elsevier B.V. All rights reserved.en_US
dc.description.sponsorshipCenter of Ring Theory and Its Applications at Ohio University; TUBITAK (The Scientific and Technological Research Council of Turkey)en_US
dc.description.sponsorshipThis article was prepared during the third author's visit to the Center of Ring Theory and Its Applications at Ohio University. She gratefully acknowledges the support of the center and the support from TUBITAK (The Scientific and Technological Research Council of Turkey). The authors wish to express their thanks to Professors D.V. Huynh and N. Er for their kind help during the preparation of this article. We also wish to thank the anonymous referee for careful reading and valuable suggestions for improvement.en_US
dc.identifier.doi10.1016/j.jpaa.2011.08.002
dc.identifier.endpage678en_US
dc.identifier.issn0022-4049
dc.identifier.issn1873-1376
dc.identifier.issue3en_US
dc.identifier.scopus2-s2.0-83855162829en_US
dc.identifier.scopusqualityQ1en_US
dc.identifier.startpage673en_US
dc.identifier.urihttps://doi.org/10.1016/j.jpaa.2011.08.002
dc.identifier.urihttps://hdl.handle.net/20.500.14619/5007
dc.identifier.volume216en_US
dc.identifier.wosWOS:000300140200013en_US
dc.identifier.wosqualityQ3en_US
dc.indekslendigikaynakWeb of Scienceen_US
dc.indekslendigikaynakScopusen_US
dc.language.isoenen_US
dc.publisherElsevieren_US
dc.relation.ispartofJournal of Pure and Applied Algebraen_US
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanıen_US
dc.rightsinfo:eu-repo/semantics/openAccessen_US
dc.titleRings whose modules have maximal or minimal projectivity domainen_US
dc.typeArticleen_US

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