理想化的互极大图

Comaximal Graph of Idealizations

设R是有1的交换环,M是R-模,R(+)M是环R对于R-模M的理想化.讨论了理想化R(+)M的理想、极大理想和可逆元与环R的理想、极大理想和可逆元之间的联系,并利用理想化的代数性质,讨论了R(+)M的互极大图的子图Γ2(R(+)M)-J(R(+)M)的直径和围长.

Let R be a commutative ring with an identity 1, M be an R-module, and R（＋）M be the idealization of the ring R by the R-module M, the relationship between ideals, maximal ideals and unit elements of idealization R（＋）M and those of ring R were discussed. The algebraic properties was also used to study the diameter and girth of the sub-graphΓ2 （R（＋）M）-J（R（＋）M） of comaximal graph of the idealization R（＋）M.