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Irreducibility of ideals in a one-dimensional analytically irreducible ring

Valentina BarucciFaten Khouja — 2010

Actes des rencontres du CIRM

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 [], [], [] to obtain this result, which is new. We finally give an algorithm to compute the components of an irredundant decomposition...

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