ARABIAN JOURNAL OF MATHEMATICS, vol.9, no.1, pp.123-135, 2020 (ESCI)
A ring R is defined to be J-normal if for any a,r is an element of R and idempotent e is an element of R, ae=0 implies Rera subset of 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 is an element of R and for any r is an element of R, R(1-e)re subset of J(R) if and only if for any n >= 1 upper triangular matrix ring Un(R) is a J-normal ring if and only if the Dorroh extension of R by Z 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 2x2 matrices over R.