Title of article
ON THE PROBABILITY OF ZERO DIVISOR ELEMENTS IN GROUP RINGS
Author/Authors
M. MOHAMMED SALIH, HAVAL Department of Mathematics - Faculty of Science - Soran University, Kawa St, Soran, Erbil, Iraq
Pages
5
From page
253
To page
257
Abstract
Let R be a non trivial finite commutative ring with identity and G be a non trivial group.
We denote by P(RG) the probability that the product of two randomly chosen elements of a finite
group ring RG is zero. We show that P(RG) <
1
4
if and only if RG Z2C2, Z3C2, Z2C3. Furthermore,
we give the upper bound and lower bound for P(RG). In particular, we present the general formula
for P(RG), where R is a finite field of characteristic p and |G| ≤
Keywords
group ring , probability , unit group , zero divisor
Journal title
International Journal of Group Theory
Serial Year
2022
Record number
2731856
Link To Document