• East Asian mathematical journal
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• v.36 no.3
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• pp.417-424
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• 2020

Huang et al. proved that the n by n upper triangular matrix ring over a domain is weakly reversible-over-center by using the property of regular matrices. In this article we provide a concrete proof which is able to be available in the related study of centers. Next we extend an example of weakly reversible-over-center, which was argued by Huang et al., to the general case.

• Communications of the Korean Mathematical Society
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• v.35 no.2
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• pp.447-454
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• 2020

The studies of reversible and NI rings have done important roles in noncommutative ring theory. A ring R shall be called QRUR if ab = 0 for a, b ∈ R implies that ba is contained in the upper nilradical of R, which is a generalization of the NI ring property. In this article we investigate the structure of QRUR rings and examine the QRUR property of several kinds of ring extensions including matrix rings and polynomial rings. We also show that if there exists a weakly semicommutative ring but not QRUR, then Köthe's conjecture does not hold.