On full affine semigroups (Q1571068)

A full semigroup consists of the set of non-negative elements of a subgroup of \(\mathbb{Z}^r\). This type of semigroups are, up to isomorphism, all the semigroups satisfying that their associated semigroup ring is normal. The authors give a classification of these semigroups which depends on the semigroup of a certain infinite group. Furthermore, they improve this classification whenever they consider semigroups of the form \(M\cap\mathbb{N}^r\). They prove that the study of this class of semigroups is equivalent to the study of subgroups \(\mathbb{Z}_{a_1}\times\mathbb{Z}_{a_r}\) such that every non-zero element has, at least, two non-zero coordinates. Finally they show that, when semigroups of \(\mathbb{N}^2\) are considered, the classification is reduced to study cyclic groups of \(\mathbb{Z}_a^2\).