Characterization of rings with nullity degree at least 14.

Let R be a finite commutative ring with nonzero identity. The nullity degree of R , denoted by z p (R) , is the probability that the multiplication of two randomly chosen elements of R is zero. In this paper, we characterize all rings R with z p (R) ≥ 1 4 . Also, we study rings R with z p (R) ≥ 1 p 2 , where p is a prime number. [ABSTRACT FROM AUTHOR]