ORDERED AND J-TRIVIAL SEMIGROUPS AS DIVISORS OF SEMIGROUPS OF LANGUAGES

被引：3

作者：

Vernitski, Alexei ^{[1
]}

机构：

[1] Univ Essex, Dept Math Sci, Colchester C04 3SQ, Essex, England

来源：

INTERNATIONAL JOURNAL OF ALGEBRA AND COMPUTATION | 2008年 / 18卷 / 07期

关键词：

Product of languages; catenation of languages; semigroup of languages; monoid of languages; J-trivial semigroup; J-trivial monoid; positively ordered semigroup; ordered monoid;

D O I：

10.1142/S021819670800486X

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

A semigroup of languages is a set of languages considered with (and closed under) the operation of catenation. In other words, semigroups of languages are subsemigroups of power-semigroups of free semigroups. We prove that a (finite) semigroup is positively ordered if and only if it is a homomorphic image, under an order-preserving homomorphism, of a (finite) semigroup of languages. Hence it follows that a finite semigroup is J-trivial if and only if it is a homomorphic image of a finite semigroup of languages.

引用

页码：1223 / 1229

页数：7

共 50 条

[1] On join irreducible J-trivial semigroups
Lee, Edmond W. H.
Rhodes, John
Steinberg, Benjamin
RENDICONTI DEL SEMINARIO MATEMATICO DELLA UNIVERSITA DI PADOVA, 2022, 147 : 43 - 78
[2] Pseudovariety joins involving J-trivial semigroups
Almeida, J
Azevedo, A
Zeitoun, M
INTERNATIONAL JOURNAL OF ALGEBRA AND COMPUTATION, 1999, 9 (01) : 99 - 112
[3] J-trivial subsemigroups of finite full transformation semigroups
Saito, T
SEMIGROUP FORUM, 1998, 57 (01) : 60 - 68
[4] Remarks on maximal J-trivial transformation semigroups on finite sets
Saito, T
SEMIGROUP FORUM, 1999, 58 (01) : 152 - 155
[5] Remarks on maximal J-trivial transformation semigroups on finite sets
T. Saito
Semigroup Forum, 1999, 58 : 152 - 155
[6] On a class of completely join prime J-trivial semigroups with unique involution
Edmond W. H. Lee
Algebra universalis, 2017, 78 : 131 - 145
[7] On a class of completely join prime J-trivial semigroups with unique involution
Lee, Edmond W. H.
ALGEBRA UNIVERSALIS, 2017, 78 (02) : 131 - 145
[8] IMPLICIT OPERATIONS ON FINITE J-TRIVIAL SEMIGROUPS AND A CONJECTURE OF SIMON,I.
ALMEIDA, J
JOURNAL OF PURE AND APPLIED ALGEBRA, 1991, 69 (03) : 205 - 218
[9] Ordered monoids and J-trivial monoids
Henckell, K
Pin, JE
ALGORITHMIC PROBLEMS IN GROUPS AND SEMIGROUPS, 2000, : 121 - 137
[10] ORDERED SEMIGROUPS, UPPER-TRIANGULAR REFLEXIVE RELATIONS AND SEMIGROUPS OF LANGUAGES
Kudryavtseva, Ganna
INTERNATIONAL JOURNAL OF ALGEBRA AND COMPUTATION, 2010, 20 (06) : 823 - 832

← 1 2 3 4 5 →