Invertible matrices over a class of semirings

被引：2
|
作者：
Dolzan, David [1 ]
机构：
[1] Univ Ljubljana, Fac Math & Phys, Dept Math, Jadranska 19, SI-1000 Ljubljana, Slovenia
来源：
JOURNAL OF ALGEBRA AND ITS APPLICATIONS | 2023年 / 22卷 / 04期
关键词：
Semiring; invertible matrix; commuting graph; idempotent; nilpotent; COMMUTING GRAPHS; DIAMETERS;
D O I：
10.1142/S0219498823500792
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We characterize the invertible matrices over a class of semirings such that the set of additively invertible elements is equal to the set of nilpotent elements. We achieve this by studying the liftings of the orthogonal sums of elements that are "almost idempotent" to those that are idempotent. Finally, we show an application of the obtained results to calculate the diameter of the commuting graph of the group of invertible matrices over the semirings in question.
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收藏
页数：11
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