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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 $v\left(I\right)$. It turns out that if $v\left(I\right)$ 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...