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.
Vengono descritti alcuni algoritmi per il calcolo del nilradicale e dei divisori dello zero di uno -monoide commutativo fintamente generato. Tali algoritmi vengono utilizzati per decidere se un ideale assegnato di uno -monoide commutativo fintamente generato è primo, radicale o primario.
@article{BUMI_2002_8_5B_3_773_0,
author = {J. C. Rosales},
title = {Commutative monoids with zero-divisors},
journal = {Bollettino dell'Unione Matematica Italiana},
volume = {5-A},
year = {2002},
pages = {773-788},
zbl = {1147.20316},
mrnumber = {1934380},
language = {en},
url = {http://dml.mathdoc.fr/item/BUMI_2002_8_5B_3_773_0}
}
Rosales, J. C. Commutative monoids with zero-divisors. Bollettino dell'Unione Matematica Italiana, Tome 5-A (2002) pp. 773-788. http://gdmltest.u-ga.fr/item/BUMI_2002_8_5B_3_773_0/
[1] -, Ideal Theory in commutative semigroups, Semigroup Forum, 30 (1984), 127-158. | MR 760214 | Zbl 0533.20032
[2] , Ideale in kommutative Halbgruppen, Mat. Sb., 35 (1929), 401-408. | JFM 55.0681.03
[3] --, Monoids determined by a homogeneus linear Diophantine equation and the half factorial property, to appear in J. Pure Appl. Algebra. | MR 1775569 | Zbl 1001.11012
[4] , Arithmetic and ideal theory of commutative semigroups, Ann. of Math., 39 (1938), 594-610. | MR 1503427 | Zbl 0019.19401
[5] -, The algebraic theory of semigroups, Amer. Math. Soc., Providence, 1961. | MR 132791 | Zbl 0111.03403
[6] , On the structure and arithmetic of finitely primary monoids, Czech. Math. J., 46 (1996), 677-695. | MR 1414602 | Zbl 0879.20032
[7] , Multiplicative ideal theory, Marcel Dekker, New York, 1972. | MR 427289 | Zbl 0248.13001
[8] , Commutative semigroup rings, Chicago Lectures in Mathematics, 1984. | MR 741678 | Zbl 0566.20050
[9] , Ideal systems. An introduction to multiplicative ideal theory, Marcel Dekker Inc., 1998. | MR 1828371 | Zbl 0953.13001
[10] -, Multiplicative theory of ideals, Academic Press, New York and London, 1971. | MR 414528 | Zbl 0237.13002
[11] , Subsemigroups of finitely generated groups with divisor-theory, Monatsh. Math., 106 (1988), 205-210. | MR 971923 | Zbl 0671.20059
[12] , The theory of finitely generated commutative semigroups, Pergamon, Oxford-Edinburgh-New York, 1965. | MR 188322 | Zbl 0133.27904
[13] , Function minimum associated to a congruence on integral -tuple space, Semigroup Forum, 51 (1995), 87-95. | MR 1337000 | Zbl 0831.20081
[14] -, Finitely generated commutative monoids, Nova Science Publishers, New York, 1999. | MR 1694173 | Zbl 0966.20028
[15] -, On decompositions of a commutative semigroup, Kodai Math. Sem. Rep., 1954, 109-112. | MR 67106 | Zbl 0058.01503
[16] , Semigroups. An introduction to the structure theory, Dekker, 1995. | MR 1350793 | Zbl 0874.20039