# The globals of pseudovarieties of ordered semigroups containing B2 and an application to a problem proposed by Pin

RAIRO - Theoretical Informatics and Applications (2010)

- Volume: 39, Issue: 1, page 1-29
- ISSN: 0988-3754

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topAlmeida, Jorge, and Escada, Ana P.. "The globals of pseudovarieties of ordered semigroups containing B2 and an application to a problem proposed by Pin." RAIRO - Theoretical Informatics and Applications 39.1 (2010): 1-29. <http://eudml.org/doc/92756>.

@article{Almeida2010,

abstract = {
Given a basis of pseudoidentities for a pseudovariety of ordered
semigroups containing the 5-element aperiodic Brandt
semigroup B2, under the natural order, it is shown that the same basis,
over the most general graph over which it can be read, defines the
global. This is used to show that the global of the pseudovariety of
level 3/2 of Straubing-Thérien's concatenation hierarchy has
infinite vertex rank.
},

author = {Almeida, Jorge, Escada, Ana P.},

journal = {RAIRO - Theoretical Informatics and Applications},

keywords = {Semigroup; pseudovariety; semigroupoid; category;
pseudoidentity; dot-depth; concatenation hierarchies.; pseudovarieties of semigroups; semigroupoids; concatenation hierarchies; ordered semigroups; bases of pseudoidentities; semidirect products},

language = {eng},

month = {3},

number = {1},

pages = {1-29},

publisher = {EDP Sciences},

title = {The globals of pseudovarieties of ordered semigroups containing B2 and an application to a problem proposed by Pin},

url = {http://eudml.org/doc/92756},

volume = {39},

year = {2010},

}

TY - JOUR

AU - Almeida, Jorge

AU - Escada, Ana P.

TI - The globals of pseudovarieties of ordered semigroups containing B2 and an application to a problem proposed by Pin

JO - RAIRO - Theoretical Informatics and Applications

DA - 2010/3//

PB - EDP Sciences

VL - 39

IS - 1

SP - 1

EP - 29

AB -
Given a basis of pseudoidentities for a pseudovariety of ordered
semigroups containing the 5-element aperiodic Brandt
semigroup B2, under the natural order, it is shown that the same basis,
over the most general graph over which it can be read, defines the
global. This is used to show that the global of the pseudovariety of
level 3/2 of Straubing-Thérien's concatenation hierarchy has
infinite vertex rank.

LA - eng

KW - Semigroup; pseudovariety; semigroupoid; category;
pseudoidentity; dot-depth; concatenation hierarchies.; pseudovarieties of semigroups; semigroupoids; concatenation hierarchies; ordered semigroups; bases of pseudoidentities; semidirect products

UR - http://eudml.org/doc/92756

ER -

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