| 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, roč. 25, 1-2, s. 259-292. ISSN 0218-1967. doi:10.1142/S021819671540010X. 2015. |
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@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, roč.~25, 1-2, s.~259-292. ISSN~0218-1967. doi:10.1142/S021819671540010X. 2015.
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