On fixed points of the lower set operator

J 2015

On fixed points of the lower set operator

ALMEIDA, Jorge, Antonio CANO, Ondřej KLÍMA a Jean-Eric PIN

Základní údaje

Originální název

On fixed points of the lower set operator

Autoři

ALMEIDA, Jorge (620 Portugalsko), Antonio CANO (724 Španělsko), Ondřej KLÍMA (203 Česká republika, garant, domácí) a Jean-Eric PIN (250 Francie)

Vydání

International Journal of Algebra and Computation, SINGAPORE, WORLD SCIENTIFIC PUBL CO PTE LTD, 2015, 0218-1967

Další údaje

Jazyk

angličtina

Typ výsledku

Článek v odborném periodiku

Obor

10101 Pure mathematics

Stát vydavatele

Singapur

Utajení

není předmětem státního či obchodního tajemství

Impakt faktor

Impact factor: 0.469

Kód RIV

RIV/00216224:14310/15:00080942

Organizační jednotka

Přírodovědecká fakulta

DOI

http://dx.doi.org/10.1142/S021819671540010X

UT WoS

000351747900011

Klíčová slova anglicky

Ordered semigroups; pseudovarieties; lower sets; power operator; inequalities; pseudoidentities

Štítky

AKR, rivok

Příznaky

Mezinárodní význam, Recenzováno

Změněno: 7. 4. 2016 14:59, Ing. Andrea Mikešková

Anotace

V originále

Lower subsets of an ordered semigroup form in a natural way an ordered semigroup. This lower set operator gives an analogue of the power operator already studied in semigroup theory. We present a complete description of the lower set operator applied to varieties of ordered semigroups. We also obtain large families of fixed points for this operator applied to pseudovarieties of ordered semigroups, including all examples found in the literature. This is achieved by constructing six types of inequalities that are preserved by the lower set operator. These types of inequalities are shown to be independent in a certain sense. Several applications are also presented, including the preservation of the period for a pseudovariety of ordered semigroups whose image under the lower set operator is proper.

Návaznosti

GBP202/12/G061, projekt VaV

Název: Centrum excelence - Institut teoretické informatiky (CE-ITI) (Akronym: CE-ITI)

Investor: Grantová agentura ČR, Centrum excelence - Institut teoretické informatiky

Citovat

ALMEIDA, Jorge, Antonio CANO, Ondřej KLÍMA a Jean-Eric PIN. On fixed points of the lower set operator. International Journal of Algebra and Computation. SINGAPORE: WORLD SCIENTIFIC PUBL CO PTE LTD, 2015, roč. 25, 1-2, s. 259-292. ISSN 0218-1967. Dostupné z: https://dx.doi.org/10.1142/S021819671540010X.

@article{1307936,
   author = {Almeida, Jorge and Cano, Antonio and Klíma, Ondřej and Pin, JeanandEric},
   article_location = {SINGAPORE},
   article_number = {1-2},
   doi = {http://dx.doi.org/10.1142/S021819671540010X},
   keywords = {Ordered semigroups; pseudovarieties; lower sets; power operator; inequalities; pseudoidentities},
   language = {eng},
   issn = {0218-1967},
   journal = {International Journal of Algebra and Computation},
   title = {On fixed points of the lower set operator},
   volume = {25},
   year = {2015}
}

TY  - JOUR
ID  - 1307936
AU  - Almeida, Jorge - Cano, Antonio - Klíma, Ondřej - Pin, Jean-Eric
PY  - 2015
TI  - On fixed points of the lower set operator
JF  - International Journal of Algebra and Computation
VL  - 25
IS  - 1-2
SP  - 259-292
EP  - 259-292
PB  - WORLD SCIENTIFIC PUBL CO PTE LTD
SN  - 02181967
KW  - Ordered semigroups
KW  - pseudovarieties
KW  - lower sets
KW  - power operator
KW  - inequalities
KW  - pseudoidentities
N2  - Lower subsets of an ordered semigroup form in a natural way an ordered semigroup. This lower set operator gives an analogue of the power operator already studied in semigroup theory. We present a complete description of the lower set operator applied to varieties of ordered semigroups. We also obtain large families of fixed points for this operator applied to pseudovarieties of ordered semigroups, including all examples found in the literature. This is achieved by constructing six types of inequalities that are preserved by the lower set operator. These types of inequalities are shown to be independent in a certain sense. Several applications are also presented, including the preservation of the period for a pseudovariety of ordered semigroups whose image under the lower set operator is proper.
ER  -

ALMEIDA, Jorge, Antonio CANO, Ondřej KLÍMA a Jean-Eric PIN. On fixed points of the lower set operator. \textit{International Journal of Algebra and Computation}. SINGAPORE: WORLD SCIENTIFIC PUBL CO PTE LTD, 2015, roč.~25, 1-2, s.~259-292. ISSN~0218-1967. Dostupné z: https://dx.doi.org/10.1142/S021819671540010X.

Podrobný výpis o publikaci