Bulletin of the
Korean Mathematical Society BKMS

We introduce the concept of $w$-zero-divisor ($w$-ZD) rings and study its related rings. In particular it is shown that an integral domain $R$ is an SM domain if and only if $R$ is a $w$-locally Noetherian $w$-ZD ring and that a commutative ring $R$ is $w$-Noetherian if and only if the polynomial ring in one indeterminate $R[X]$ is a $w$-ZD ring. Finally we characterize universally zero divisor rings in terms of $w$-ZD modules.

Keywords: zero divisor, zero divisor ring, zero divisor module, universally zero divisor ring, w-operation

MSC numbers: Primary 13A15; Secondary 13E99, 13F05