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.
引用
收藏
页数：11
相关论文
共 15 条
  • [1] On the diameters of commuting graphs
    Akbari, S.
    Mohammadian, A.
    Radjavi, H.
    Raja, P.
    [J]. LINEAR ALGEBRA AND ITS APPLICATIONS, 2006, 418 (01) : 161 - 176
  • [2] Commuting Graphs of Matrix Algebras
    Akbari, S.
    Bidkhori, H.
    Mohammadian, A.
    [J]. COMMUNICATIONS IN ALGEBRA, 2008, 36 (11) : 4020 - 4031
  • [3] Baccelli F., 1998, IDEMPOTENCY, P171
  • [4] Cuninghame-Green R. A., 2012, MINIMAX ALGEBRA, V166
  • [5] The commuting graphs of finite rings
    Dolzan, David
    [J]. PUBLICATIONES MATHEMATICAE-DEBRECEN, 2019, 95 (1-2): : 123 - 131
  • [6] On diameter of the commuting graph of a full matrix algebra over a finite field
    Dolzan, David
    Bukovsek, Damjana Kokol
    Kuzma, Bojan
    Oblak, Polona
    [J]. FINITE FIELDS AND THEIR APPLICATIONS, 2016, 37 : 36 - 45
  • [7] Diameters of commuting graphs of matrices over semirings
    Dolzan, David
    Bukovsek, Damjana Kokol
    Oblak, Polona
    [J]. SEMIGROUP FORUM, 2012, 84 (02) : 365 - 373
  • [8] Commuting graphs of matrices over semirings
    Dolzan, David
    Oblak, Polona
    [J]. LINEAR ALGEBRA AND ITS APPLICATIONS, 2011, 435 (07) : 1657 - 1665
  • [9] Invertible and nilpotent matrices over antirings
    Dolzan, David
    Oblak, Polona
    [J]. LINEAR ALGEBRA AND ITS APPLICATIONS, 2009, 430 (01) : 271 - 278
  • [10] Hebisch U., 1998, SEMIRINGS ALGEBRAIC, V5
12