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dc.contributor.authorKöse, H.
dc.contributor.authorKurtulmaz, Yosum
dc.contributor.authorHarmancı, A.
dc.date.accessioned2021-02-27T16:47:30Z
dc.date.available2021-02-27T16:47:30Z
dc.date.issued2020
dc.identifier.issn2193-5343
dc.identifier.urihttp://hdl.handle.net/11693/75625
dc.description.abstractA ring R is defined to be J-normal if for any a,r∈Ra,r∈R and idempotent e∈Re∈R, ae=0ae=0 implies Rera⊆J(R)Rera⊆J(R), where J(R) is the Jacobson radical of R. The class of J-normal rings lies between the classes of weakly normal rings and left min-abel rings. It is proved that R is J-normal if and only if for any idempotent e∈Re∈R and for any r∈Rr∈R, R(1−e)re⊆J(R)R(1−e)re⊆J(R) if and only if for any n≥1n≥1, the n×nn×n upper triangular matrix ring Un(R)Un(R) is a J-normal ring if and only if the Dorroh extension of R by ZZ is J-normal. We show that R is strongly regular if and only if R is J-normal and von Neumann regular. For a J-normal ring R, it is obtained that R is clean if and only if R is exchange. We also investigate J-normality of certain subrings of the ring of 2×22×2 matrices over R.en_US
dc.language.isoEnglishen_US
dc.source.titleArabian Journal of Mathematicsen_US
dc.relation.isversionofhttps://dx.doi.org/10.1007/s40065-018-0231-7en_US
dc.titleRings having normality in terms of the Jacobson radicalen_US
dc.typeArticleen_US
dc.citation.spage123en_US
dc.citation.epage135en_US
dc.citation.volumeNumber9en_US
dc.citation.issueNumber1en_US
dc.identifier.doi10.1007/s40065-018-0231-7en_US
dc.publisherSpringeren_US
dc.contributor.bilkentauthorKurtulmaz, Yosum


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