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PDF(472 KB)
PDF(472 KB)
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
设R是一个环，其上的理想包含图，记为ΓI（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Γi（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 ΓI(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 Γi(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 Fq be denoted by Mn(Fq). In this paper, both the automorphisms of ΓI(Mn(Fq)) and the automorphisms of Γi(Mn(Fq)) are characterized.
理想包含图 / 理想关系图 / 图自同构 / 全矩阵环 / 有限域 {{custom_keyword}} /
inclusion ideal graph / ideal-relation graph / graph automorphism / total matrix ring / finite field {{custom_keyword}} /
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国家自然科学基金资助项目（11571360）
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