理想化的互极大图

摘要

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.