Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4598365 | Journal of Pure and Applied Algebra | 2007 | 8 Pages |
Abstract
For a commutative ring RR with zero-divisors Z(R)Z(R), the zero-divisor graph of RR is Γ(R)=Z(R)−{0}Γ(R)=Z(R)−{0}, with distinct vertices xx and yy adjacent if and only if xy=0xy=0. In this paper, we characterize when either diam(Γ(R))≤2 or gr(Γ(R))≥4. We then use these results to investigate the diameter and girth for the zero-divisor graphs of polynomial rings, power series rings, and idealizations.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
David F. Anderson, S.B. Mulay,