Semigroup identities of tropical matrix semigroups of maximal rank

Zur Izhakian

doi:10.1007/s00233-015-9765-6

Semigroup identities of tropical matrix semigroups of maximal rank

Zur Izhakian^*

^*Corresponding author for this work

Mathematical Science

Research output: Contribution to journal › Article › peer-review

7 Citations (Scopus)

Abstract

We show that any semigroup of n-by-n tropical matrices whose elements all have rank n (i.e., a nonsingular semigroup) satisfies a class of nontrivial semigroup identities. These identities generalize the identities satisfied by the monoid of all n-by-n triangular tropical matrices.

Original language	English
Pages (from-to)	712-732
Number of pages	21
Journal	Semigroup Forum
Volume	92
Issue number	3
Early online date	30 Nov 2015
DOIs	https://doi.org/10.1007/s00233-015-9765-6
Publication status	Published - 1 Jun 2016

Keywords

Nonsingular matrices
Rank-maximal semigroups
Semigroup identities
Semigroup representations
Semigroup varieties
Tropical (max-plus) matrix algebra

Access to Document

10.1007/s00233-015-9765-6Licence: Unspecified

Cite this

@article{6ace3911f7aa4ce5aa94e2dcd7dd7b1f,

title = "Semigroup identities of tropical matrix semigroups of maximal rank",

abstract = "We show that any semigroup of n-by-n tropical matrices whose elements all have rank n (i.e., a nonsingular semigroup) satisfies a class of nontrivial semigroup identities. These identities generalize the identities satisfied by the monoid of all n-by-n triangular tropical matrices.",

keywords = "Nonsingular matrices, Rank-maximal semigroups, Semigroup identities, Semigroup representations, Semigroup varieties, Tropical (max-plus) matrix algebra",

author = "Zur Izhakian",

note = "Acknowledgments The author would like to thank the referee for his comments and helpful suggestions.",

year = "2016",

month = jun,

day = "1",

doi = "10.1007/s00233-015-9765-6",

language = "English",

volume = "92",

pages = "712--732",

journal = "Semigroup Forum",

issn = "0037-1912",

publisher = "Springer New York",

number = "3",

}

TY - JOUR

T1 - Semigroup identities of tropical matrix semigroups of maximal rank

AU - Izhakian, Zur

N1 - Acknowledgments The author would like to thank the referee for his comments and helpful suggestions.

PY - 2016/6/1

Y1 - 2016/6/1

N2 - We show that any semigroup of n-by-n tropical matrices whose elements all have rank n (i.e., a nonsingular semigroup) satisfies a class of nontrivial semigroup identities. These identities generalize the identities satisfied by the monoid of all n-by-n triangular tropical matrices.

AB - We show that any semigroup of n-by-n tropical matrices whose elements all have rank n (i.e., a nonsingular semigroup) satisfies a class of nontrivial semigroup identities. These identities generalize the identities satisfied by the monoid of all n-by-n triangular tropical matrices.

KW - Nonsingular matrices

KW - Rank-maximal semigroups

KW - Semigroup identities

KW - Semigroup representations

KW - Semigroup varieties

KW - Tropical (max-plus) matrix algebra

UR - http://www.scopus.com/inward/record.url?scp=84948961732&partnerID=8YFLogxK

U2 - 10.1007/s00233-015-9765-6

DO - 10.1007/s00233-015-9765-6

M3 - Article

AN - SCOPUS:84948961732

VL - 92

SP - 712

EP - 732

JO - Semigroup Forum

JF - Semigroup Forum

SN - 0037-1912

IS - 3

ER -

Semigroup identities of tropical matrix semigroups of maximal rank

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this