Commutative monoids with zero-divisors

J. C. Rosales

Bollettino dell'Unione Matematica Italiana (2002)

  • Volume: 5-B, Issue: 3, page 773-788
  • ISSN: 0392-4041

Abstract

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We describe algorithms for computing the nilradical and the zero-divisors of a finitely generated commutative ∅ -monoid. These algorithms will be used for deciding if a given ideal of a finitely generated commutative ∅ -monoid is prime, radical or primary.

How to cite

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Rosales, J. C.. "Commutative monoids with zero-divisors." Bollettino dell'Unione Matematica Italiana 5-B.3 (2002): 773-788. <http://eudml.org/doc/195995>.

@article{Rosales2002,
abstract = {We describe algorithms for computing the nilradical and the zero-divisors of a finitely generated commutative $\emptyset$-monoid. These algorithms will be used for deciding if a given ideal of a finitely generated commutative $\emptyset$-monoid is prime, radical or primary.},
author = {Rosales, J. C.},
journal = {Bollettino dell'Unione Matematica Italiana},
keywords = {zero-divisors; finitely generated commutative zero-monoids; algorithms; ideals},
language = {eng},
month = {10},
number = {3},
pages = {773-788},
publisher = {Unione Matematica Italiana},
title = {Commutative monoids with zero-divisors},
url = {http://eudml.org/doc/195995},
volume = {5-B},
year = {2002},
}

TY - JOUR
AU - Rosales, J. C.
TI - Commutative monoids with zero-divisors
JO - Bollettino dell'Unione Matematica Italiana
DA - 2002/10//
PB - Unione Matematica Italiana
VL - 5-B
IS - 3
SP - 773
EP - 788
AB - We describe algorithms for computing the nilradical and the zero-divisors of a finitely generated commutative $\emptyset$-monoid. These algorithms will be used for deciding if a given ideal of a finitely generated commutative $\emptyset$-monoid is prime, radical or primary.
LA - eng
KW - zero-divisors; finitely generated commutative zero-monoids; algorithms; ideals
UR - http://eudml.org/doc/195995
ER -

References

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  11. LETTL, G., Subsemigroups of finitely generated groups with divisor-theory, Monatsh. Math., 106 (1988), 205-210. Zbl0671.20059MR971923
  12. RÉDEI, L., The theory of finitely generated commutative semigroups, Pergamon, Oxford-Edinburgh-New York, 1965. Zbl0133.27904MR188322
  13. ROSALES, J. C., Function minimum associated to a congruence on integral n -tuple space, Semigroup Forum, 51 (1995), 87-95. Zbl0831.20081MR1337000
  14. ROSALES, J. C.- GARCÍA-SÁNCHEZ, P. A., Finitely generated commutative monoids, Nova Science Publishers, New York, 1999. Zbl0966.20028MR1694173
  15. TAMURA, T.- KIMURA, N., On decompositions of a commutative semigroup, Kodai Math. Sem. Rep., 1954, 109-112. Zbl0058.01503MR67106
  16. GRILLET, P. A., Semigroups. An introduction to the structure theory, Dekker, 1995. Zbl0874.20039MR1350793

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