I’d like to make something more explicit than I have. An effective Cartier divisor on a scheme is a closed subscheme locally cut out by one function, and that function is not a zero-divisor. (Translation: the zero-set does not contain any associated points.) PicX = group of line bundles = Cartier divisors modulo linear equivalence = Cartier divisors modulo principal Cartier divisors. We get a m...

L-zero-divisor graphs of L-commutative rings have been introduced and studied in [5]. Here we consider L-zero-divisor graphs of a finite direct product of L-commutative rings. Specifically, we look at the preservation, or lack thereof, of the diameter and girth of the L-zirodivisor graph of a L-ring when extending to a finite direct product of L-commutative rings.

For a commutative semigroup S with 0, the zero-divisor graph of S denoted by Γ(S) is the graph whose vertices are nonzero zero-divisor of S, and two vertices x, y are adjacent in case xy = 0 in S. In this paper we study median and center of this graph. Also we show that if Ass(S) has more than two elements, then the girth of Γ(S) is three.