Bulletin of the
Korean Mathematical Society BKMS

{This note focuses on a ring property in which upper and lower nilradicals coincide, as a generalizations of symmetric rings. The concept of symmetric ideal and ring in the noncommutative ring theory was initially introduced by Lambek, as an extension of the usual commutative ideal theory. The investigation of symmetric rings provided many useful results to the study in the noncommutative ring theory. So the results obtained from this study may be applicable to observing the structure of zero divisors in various kinds of algebraic systems containing matrix rings and polynomial rings.}

Keywords: weak nil-symmetric ring, upper and lower nilradicals coincide, zero divisor, symmetric ring, matrix ring, polynomial ring

MSC numbers: 16U80, 16S70