no. 2
Irreducibility of ideals in a one-dimensional analytically irreducible ring
Barucci, Valentina1 ; Khouja, Faten2
1 Dipartimento di Matematica, Sapienza, Università di Roma, Piazzale A. Moro 2, 00185 Rome, ITALY
2 Department of Mathematics, Faculty of Sciences, 5000 Monastir, TUNISIA.
Actes des rencontres du CIRM, Troisième Rencontre Internationale sur les Polynômes à Valeurs Entières, Tome 2 (2010) no. 2, pp. 91-93

Let R be a one-dimensional analytically irreducible ring and let I be an integral ideal of R. We study the relation between the irreducibility of the ideal I in R and the irreducibility of the corresponding semigroup ideal v(I). It turns out that if v(I) is irreducible, then I is irreducible, but the converse does not hold in general. We collect some known results taken from [5], [4], [3] to obtain this result, which is new. We finally give an algorithm to compute the components of an irredundant decomposition of a nonzero ideal.

Publié le :
DOI : 10.5802/acirm.40
Classification : 13A15, 13H10
Keywords: Numerical semigroup, canonical ideal, irreducible ideal.

Barucci, Valentina 1 ; Khouja, Faten 2

1 Dipartimento di Matematica, Sapienza, Università di Roma, Piazzale A. Moro 2, 00185 Rome, ITALY
2 Department of Mathematics, Faculty of Sciences, 5000 Monastir, TUNISIA. 
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     title = {Irreducibility of ideals in a one-dimensional analytically irreducible ring},
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     year = {2010},
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Barucci, Valentina; Khouja, Faten. Irreducibility of ideals in a one-dimensional analytically irreducible ring. Actes des rencontres du CIRM, Troisième Rencontre Internationale sur les Polynômes à Valeurs Entières, Tome 2 (2010) no. 2, pp. 91-93. doi: 10.5802/acirm.40

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[5] E. Kunz, Introduction to Commutative Algebra and Algebraic Geometry. Birkhauser, 1984. | DOI

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