您的位置：山东大学 -> 科技期刊社 -> 《山东大学学报（理学版）》

《山东大学学报(理学版)》 ›› 2022, Vol. 57 ›› Issue (2): 50-55.doi: 10.6040/j.issn.1671-9352.0.2021.412

• • 上一篇    

Tropical矩阵半群

王晶,宫春梅*   

  1. 西安建筑科技大学理学院, 陕西 西安 710055
  • 发布日期:2022-01-07
  • 作者简介:王晶(1997— ), 女, 硕士研究生, 研究方向为半群代数理论. E-mail:2157704087@qq.com*通信作者简介:宫春梅(1981— ), 女, 博士, 副教授, 研究方向为半群代数理论. E-mail:meigongchu@163.com
  • 基金资助:
    国家自然科学基金青年资助项目(12001418);陕西省教育厅基金项目(18JK0442)

Tropical matrix semigroups

WANG Jing, GONG Chun-mei*   

  1. School of Science, Xian University of Architecture and Technology, Xian 710055, Shaanxi, China
  • Published:2022-01-07

PDF (PC)

351

摘要： 研究了tropical矩阵乘法半群的(*)-Green关系和正则性,给出了tropical矩阵乘法半群上R*、D *关系的等价刻画,讨论了上三角tropical矩阵乘法半群的正则性。

关键词: tropical半环, 矩阵半群, Green关系, 正则性

Abstract: The(*)-Greens relations and regularity of tropical matrix multiplicative semigroups are studied. The equivalent characterizations of the R* and D * relations on tropical matrix multiplicative semigroups are given, the regularity properties of the upper triangular tropical matrix multiplicative semigroups are discussed.

Key words: tropical semiring, matrix semigroups, Greens relation, regularity

中图分类号: 

  • O152.7
[1] GREEN R C. Minimax algebra[M] //Lecture Notes in Economics and Mathematical Systems. Berlin: Springer, 1979.
[2] OLSDER G J, ROOS C. Cramer and Cayley-Hamilton in the max algebra[J]. Linear Algebra and Its Applications, 1988, 101(1):87-108.
[3] ILIN S N. Regularity criterion for complete matrix semirings[J]. Mathematical Notes, 2001, 70(3):329-336.
[4] BUTKOVIC P. Max-linear systems: theory and algorithms[M]. London: Springer, 2010.
[5] JOHNSON M, KAMBITES M. Multiplicative structure of 2×2 tropical matrices[J]. Linear Algebra and Its Applications, 2011, 435(7):1612-1625.
[6] HOLLINGS C, KAMBITES M. Tropical matrix duality and Greens D relation[J]. Journal of the London Mathematical Society, 2012(2):520-538.
[7] JOHNSON M, KAMBITES M. Greens J-order and the rank of tropical matrices[J]. Journal of Pure and Applied Algebra. 2013, 217(2):280-292.
[8] IZHAKIAN Z, JOHNSON M, KAMBITES M. Pure dimension and projectivity of tropical polytopes[J]. Advances in Mathematics, 2016, 303:1236-1263.
[9] IZHAKIAN Z, JOHNSON M, KAMBITES M. Tropical matrix groups[J]. Semigroup Forum, 2018, 96:178-196.
[10] GOULD V, JOHNSON M, NAZ M. Matrix semigroups over semirings[J]. International Journal of Algebra and Computation, 2020, 30(20):267-337.
[11] IZHAKIAN Z, MARGOLI S W. Semigroup identities in the monoid of two-by-two tropical matrices[J]. Semigroup Forum, 2010, 80(2):191-218.
[12] HOWIE J M. Fundamentals of sermigroup theory[M]. Oxford: Clarendon Press, 1995.
[13] PASTIJN F. A representation of a semigroup by a semigroup of matrices over a group with zero[J]. Semigroup Forum, 1975, 10(1):238-249.
[14] FOUNTAIN J B. Abundant semigroups[J]. Proceeding of the London Mathematical Society, 1982, 44(1):103-129.
[15] WILDING D, JOHNSON M, KAMBITES M. Exact rings and semirings[J]. Journal of Algebra, 2013, 388(4):324-337.
[16] WILDING D. Linear algebra over semirings[D]. Manchester: University of Manchester, 2014.
[1] 李有玲,汪璇. 带衰退记忆的非自治非经典扩散方程的吸引子[J]. 《山东大学学报(理学版)》, 2021, 56(9): 66-80.
[2] 王海权,种鸽子. 两分量Novikov系统初值问题解的局部Gevrey正则性与解析性[J]. 《山东大学学报(理学版)》, 2020, 55(6): 56-63.
[3] 徐秀娟,闫硕,朱叶青. 一类非齐次A-调和方程很弱解的全局正则性[J]. 《山东大学学报(理学版)》, 2020, 55(2): 48-56.
[4] 钱鑫强,王开荣. 非光滑多目标区间优化的最优性条件[J]. 《山东大学学报(理学版)》, 2020, 55(11): 26-34.
[5] 杜广伟. 具有次临界增长的椭圆障碍问题解的正则性[J]. 山东大学学报（理学版）, 2018, 53(6): 57-63.
[6] 宫春梅,冯丽霞,任学明. 完全J *,~-单半群上的(*,~)-好同余[J]. 山东大学学报（理学版）, 2018, 53(6): 11-16.
[7] 李小娟,高强. 次线性期望框架下乘积空间的正则性[J]. 山东大学学报（理学版）, 2018, 53(4): 66-75.
[8] 苏玉,孔祥智*. LρC-正则半群[J]. J4, 2011, 46(4): 68-69.
[9] 代丽美. Hessian方程黏性解的正则性[J]. J4, 2010, 45(9): 62-64.
[10] 刘开振 孔祥智. 半超富足半群的结构[J]. J4, 2010, 45(1): 86-88.
[11] 丁 月,孔祥智 . H#-富足半群[J]. J4, 2008, 43(4): 55-57 .
Viewed
Full text


Abstract

Cited
  Shared   
  Discussed   
No Suggested Reading articles found!
版权所有 © 2018 《山东大学学报(理学版)》编辑部　
地址: 山东省济南市山大南路27号山东大学中心校区（250100）　电话: +86-0531-88366917　E-mail: xblxb@sdu.edu.cn
本系统由北京玛格泰克科技发展有限公司设计开发