Irreducibility of ideals in a one-dimensional analytically irreducible ring
Let be a one-dimensional analytically irreducible ring and let be an integral ideal of . We study the relation between the irreducibility of the ideal in and the irreducibility of the corresponding semigroup ideal . It turns out that if is irreducible, then 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...