全矩阵环上理想包含图的自同构群  

Automorphisms of an Inclusion Ideal Graph over a Total Matrix Ring

作　　者：陈莉 

机构地区：[1]中国矿业大学数学学院

出　　处：《数学学报（中文版）》2018年第1期135-142,共8页Acta Mathematica Sinica：Chinese Series

基　　金：国家自然科学基金资助项目(11571360)

摘　　要：设R是一个环，其上的理想包含图，记为ГI（R），是一个有向图，它以R的非平凡左理想为顶点，从R的左理想I1到I2有一条有向边当且仅当I1真包含于I2．环R上的理想关系图，记为Гi（R），也是一个有向图，它以R为顶点集，从R中元素A到B有一条有向边当且仅当A生成的左理想真包含于B生成的左理想．设Fq为有限域，其上n阶全矩阵环记为Mn（Fq），本文刻画了环Mn（Fq）上的理想包含图以及理想关系图的任意自同构．The inclusion ideal graph of a ring R, written as ГI（R）, is a directed graph which has all nontrivial left rings of R as vertex set and there is a directed edge from a vertex I1 to a distinct vertex I2 if and only if I1 is properly contained in I2. In addition, the ideal-relation graph of a ring R, written as Fi（R）, is also a directed graph which has R as vertex set and there is a directed edge from a vertex A to a distinct vertex B if and only if the left ideal of R generated by A is properly contained in the left ideal generated by B. Let Fq be a finite field, the set of n × n matrices over Fa be denoted by Mn（Fq）. In this paper, both the automorphisms of ГI（Mn（Fq）） and the automorphisms of Гi （Mn（Fq）） are characterized.

关 键 词：理想包含图 理想关系图 图自同构 全矩阵环 有限域 

分 类 号：O157[理学—数学]