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

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

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
DOIs	https://doi.org/10.1007/s00233-015-9765-6
State	Published - 1 Jun 2016
Externally published	Yes

Keywords

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

All Science Journal Classification (ASJC) codes

Algebra and Number Theory

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10.1007/s00233-015-9765-6

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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",

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T1 - Semigroup identities of tropical matrix semigroups of maximal rank

AU - Izhakian, Zur

PY - 2016/6/1

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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

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U2 - 10.1007/s00233-015-9765-6

DO - 10.1007/s00233-015-9765-6

M3 - مقالة

SN - 0037-1912

VL - 92

SP - 712

EP - 732

JO - Semigroup Forum

JF - Semigroup Forum

IS - 3

ER -

Semigroup identities of tropical matrix semigroups of maximal rank

Abstract

Keywords

All Science Journal Classification (ASJC) codes

Access to Document

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