Principal ideals of finitely generated commutative monoids

José Carlos Rosales; Juan Ignacio García-García

Czechoslovak Mathematical Journal (2002)

  • Volume: 52, Issue: 1, page 75-85
  • ISSN: 0011-4642

Abstract

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We study the semigroups isomorphic to principal ideals of finitely generated commutative monoids. We define the concept of finite presentation for this kind of semigroups. Furthermore, we show how to obtain information on these semigroups from their presentations.

How to cite

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Rosales, José Carlos, and García-García, Juan Ignacio. "Principal ideals of finitely generated commutative monoids." Czechoslovak Mathematical Journal 52.1 (2002): 75-85. <http://eudml.org/doc/30686>.

@article{Rosales2002,
abstract = {We study the semigroups isomorphic to principal ideals of finitely generated commutative monoids. We define the concept of finite presentation for this kind of semigroups. Furthermore, we show how to obtain information on these semigroups from their presentations.},
author = {Rosales, José Carlos, García-García, Juan Ignacio},
journal = {Czechoslovak Mathematical Journal},
keywords = {monoid; ideal; cancellative; torsion free; finitely generated commutative monoids; principal ideals; cancellative monoids; presentations},
language = {eng},
number = {1},
pages = {75-85},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Principal ideals of finitely generated commutative monoids},
url = {http://eudml.org/doc/30686},
volume = {52},
year = {2002},
}

TY - JOUR
AU - Rosales, José Carlos
AU - García-García, Juan Ignacio
TI - Principal ideals of finitely generated commutative monoids
JO - Czechoslovak Mathematical Journal
PY - 2002
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 52
IS - 1
SP - 75
EP - 85
AB - We study the semigroups isomorphic to principal ideals of finitely generated commutative monoids. We define the concept of finite presentation for this kind of semigroups. Furthermore, we show how to obtain information on these semigroups from their presentations.
LA - eng
KW - monoid; ideal; cancellative; torsion free; finitely generated commutative monoids; principal ideals; cancellative monoids; presentations
UR - http://eudml.org/doc/30686
ER -

References

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  7. The theory of finitely commutative semigroups, Pergamon, Oxford-Edinburgh-New York, 1965. (1965) MR0188322
  8. Finitely generated commutative monoids, vol. xiv, Nova Science Publishers, New York, 1999. (1999) MR1694173
  9. 10.1080/00927879608825809, Comm. Algebra 24 (1996), 4217–4224. (1996) MR1414579DOI10.1080/00927879608825809
  10. 10.1007/BF02573522, Semigroup Forum 50 (1995), 251–262. (1995) MR1315517DOI10.1007/BF02573522
  11. 10.1007/BF02780180, Israel J. Math. 113 (1999), 269–283. (1999) MR1729450DOI10.1007/BF02780180

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