Properties of the subsemigroups of the bicyclic monoid

L. Descalço; N. Ruškuc

Czechoslovak Mathematical Journal (2008)

  • Volume: 58, Issue: 2, page 311-330
  • ISSN: 0011-4642

Abstract

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In this paper we study some properties of the subsemigroups of the bicyclic monoid B, by using a recent description of its subsemigroups. We start by giving necessary and sufficient conditions for a subsemigroup to be finitely generated. Then we show that all finitely generated subsemigroups are automatic and finitely presented. Finally we prove that a subsemigroup of B is residually finite if and only if it does not contain a copy of B.

How to cite

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Descalço, L., and Ruškuc, N.. "Properties of the subsemigroups of the bicyclic monoid." Czechoslovak Mathematical Journal 58.2 (2008): 311-330. <http://eudml.org/doc/31212>.

@article{Descalço2008,
abstract = {In this paper we study some properties of the subsemigroups of the bicyclic monoid B, by using a recent description of its subsemigroups. We start by giving necessary and sufficient conditions for a subsemigroup to be finitely generated. Then we show that all finitely generated subsemigroups are automatic and finitely presented. Finally we prove that a subsemigroup of B is residually finite if and only if it does not contain a copy of B.},
author = {Descalço, L., Ruškuc, N.},
journal = {Czechoslovak Mathematical Journal},
keywords = {bicyclic monoid; subsemigroup; generators; defining relations; automatic structures; bicyclic monoid; subsemigroups; generators; defining relations; automatic structures; finitely generated semigroups; automatic semigroups; finitely presented semigroups; residually finite semigroups},
language = {eng},
number = {2},
pages = {311-330},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Properties of the subsemigroups of the bicyclic monoid},
url = {http://eudml.org/doc/31212},
volume = {58},
year = {2008},
}

TY - JOUR
AU - Descalço, L.
AU - Ruškuc, N.
TI - Properties of the subsemigroups of the bicyclic monoid
JO - Czechoslovak Mathematical Journal
PY - 2008
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 58
IS - 2
SP - 311
EP - 330
AB - In this paper we study some properties of the subsemigroups of the bicyclic monoid B, by using a recent description of its subsemigroups. We start by giving necessary and sufficient conditions for a subsemigroup to be finitely generated. Then we show that all finitely generated subsemigroups are automatic and finitely presented. Finally we prove that a subsemigroup of B is residually finite if and only if it does not contain a copy of B.
LA - eng
KW - bicyclic monoid; subsemigroup; generators; defining relations; automatic structures; bicyclic monoid; subsemigroups; generators; defining relations; automatic structures; finitely generated semigroups; automatic semigroups; finitely presented semigroups; residually finite semigroups
UR - http://eudml.org/doc/31212
ER -

References

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