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Buyukasik, Engin; Demir, Ozlem; Diril, Muge
<?xml version='1.0' encoding='utf-8'?> <resource xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns="http://datacite.org/schema/kernel-4" xsi:schemaLocation="http://datacite.org/schema/kernel-4 http://schema.datacite.org/meta/kernel-4.1/metadata.xsd"> <identifier identifierType="URL">https://aperta.ulakbim.gov.tr/record/5917</identifier> <creators> <creator> <creatorName>Buyukasik, Engin</creatorName> <givenName>Engin</givenName> <familyName>Buyukasik</familyName> <affiliation>Izmir Inst Technol, Dept Math, TR-35430 Izmir, Turkey</affiliation> </creator> <creator> <creatorName>Demir, Ozlem</creatorName> <givenName>Ozlem</givenName> <familyName>Demir</familyName> <affiliation>Izmir Inst Technol, Dept Math, TR-35430 Izmir, Turkey</affiliation> </creator> <creator> <creatorName>Diril, Muge</creatorName> <givenName>Muge</givenName> <familyName>Diril</familyName> <affiliation>Izmir Inst Technol, Dept Math, TR-35430 Izmir, Turkey</affiliation> </creator> </creators> <titles> <title>On Simple-Direct Modules</title> </titles> <publisher>Aperta</publisher> <publicationYear>2020</publicationYear> <dates> <date dateType="Issued">2020-01-01</date> </dates> <resourceType resourceTypeGeneral="Text">Journal article</resourceType> <alternateIdentifiers> <alternateIdentifier alternateIdentifierType="url">https://aperta.ulakbim.gov.tr/record/5917</alternateIdentifier> </alternateIdentifiers> <relatedIdentifiers> <relatedIdentifier relatedIdentifierType="DOI" relationType="IsIdenticalTo">10.1080/00927872.2020.1821207</relatedIdentifier> </relatedIdentifiers> <rightsList> <rights rightsURI="http://www.opendefinition.org/licenses/cc-by">Creative Commons Attribution</rights> <rights rightsURI="info:eu-repo/semantics/openAccess">Open Access</rights> </rightsList> <descriptions> <description descriptionType="Abstract">Recently, in a series of papers "simple" versions of direct-injective and direct-projective modules have been investigated. These modules are termed as "simple-direct-injective" and "simple-direct-projective," respectively. In this paper, we give a complete characterization of the aforementioned modules over the ring of integers and over semilocal rings. The ring is semilocal if and only if every right module with zero Jacobson radical is simple-direct-projective. The rings whose simple-direct-injective right modules are simple-direct-projective are fully characterized. These are exactly the left perfect right H-rings. The rings whose simple-direct-projective right modules are simple-direct-injective are right max-rings. For a commutative Noetherian ring, we prove that simple-direct-projective modules are simple-direct-injective if and only if simple-direct-injective modules are simple-direct-projective if and only if the ring is Artinian. Various closure properties and some classes of modules that are simple-direct-injective (resp. projective) are given.</description> </descriptions> </resource>
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