JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2022, Vol. 57 ›› Issue (2): 50-55.doi: 10.6040/j.issn.1671-9352.0.2021.412

Previous Articles    

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)

327

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

CLC Number: 

  • 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] LI You-ling, WANG Xuan. Attractors for the non-autonomous nonclassical diffusion equation with fading memory [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2021, 56(9): 66-80.
[2] WANG Hai-quan, CHONG Ge-zi. Local Gevrey regularity and analyticity of the solutions to the initial value problem associated with the two-component Novikov system [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2020, 55(6): 56-63.
[3] XU Xiu-juan, YAN Shuo, ZHU Ye-qing. Global regularity for very weak solutions to non-homogeneous A-harmonic equation [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2020, 55(2): 48-56.
[4] QIAN Xin-qiang, WANG Kai-rong. Optimality conditions on nonsmooth vector interval-valued optimization [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2020, 55(11): 26-34.
[5] QI Ping, WANG Fu-cheng, WANG Bi-qing, LIANG Chang-yong. Dynamic level scheduling algorithm for cloud computing based on failure regularity-aware [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2019, 54(1): 103-115.
[6] . Regularity for solutions of elliptic obstacle problems with subcritical growth [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2018, 53(6): 57-63.
[7] GONG Chun-mei, FENG Li-xia, REN Xue-ming. (*,~)-good congruences on completely J *,~-simple semigroups [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2018, 53(6): 11-16.
[8] LI Xiao-juan, GAO Qiang. Regularity for product space under sublinear expectation framework [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2018, 53(4): 66-75.
[9] LI Feng-ping, CHEN Guang-xia. Regularity criteria for weak solutions to the 3D magneto-micropolar fluid equations [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2015, 50(05): 60-67.
[10] GUO Jing1, CHEN Xiang-en1, WANG Zhi-wen2. Irregular assignments of the union of several vertex-disjoint #br# paths with order n [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2014, 49(06): 18-25.
[11] LIN Rong1,2, FAN Cheng-xian3. Function P-sets and dynamic characteristics of information regularity [J]. J4, 2012, 47(1): 121-126.
[12] DAI Li-mei. Regularity of viscosity solutions to Hessian equations [J]. J4, 2010, 45(9): 62-64.
[13] JIAO Tie-Ke. The eventually regularity on a class subsemirings of a semiring [J]. J4, 2009, 44(8): 56-57.
[14] LIU Hong-ping,MENG Guang-wu . F*-Paracompactness in L-topological spaces [J]. J4, 2008, 43(3): 75-79 .
Viewed
Full text


Abstract

Cited
  Shared   
  Discussed   
No Suggested Reading articles found!
Copyright 2018 © Editorial office of JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)
Supported by Beijing Magtech Co.Ltd