环的直积的零因子图

Zero-divisor Graph of the Direct Product of Commutative Rings

研究了交换环的直积R1×R2的零因子图.对于交换环R1和R2,讨论了零因子图Γ(R1×R2)的直径与围长,分别确定了当图Γ(R1×R2)的直径为1,2,3时,对应的交换环R1和R2的代数结构,并给出了环的等价表述.

The zero-divisor graphs of the direct product of commutative rings is studied. For any commutative ring R1 and R2, attention is focused on the diameter of R1×R2, and the algebraic structure of R1 ,RE, is determined where the diameter of F（R1×R2 ） is 1,2, or 3. Furthermore, the equivalent characterization of the diameter of the zero-divisor graph of R1×R2 is presented.