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 finally give an algorithm to compute the components of an irredundant decomposition of a nonzero ideal.
Irreducibility of ideals in a one-dimensional analytically irreducible ring / Barucci, Valentina; Faten, Khouja. - ELETTRONICO. - 2:2(2010), pp. 91-93. (Intervento presentato al convegno Third International Meeting on Integer-Valued Polynomials tenutosi a Marsiglia nel 29 novembre - 3 dicembre 2010) [10.5802/acirm.40].
Irreducibility of ideals in a one-dimensional analytically irreducible ring
BARUCCI, Valentina;
2010
Abstract
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 finally give an algorithm to compute the components of an irredundant decomposition of a nonzero ideal.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
