A finitely generated commutative monoid is uniquely presented if it has a unique minimal
presentation. We give necessary and sufficient conditions for finitely generated …

We give a new classification of monomial curves in A 4 (k). It relies on the detection of those
binomials and monomials that have to appear in every system of binomial generators of the …

In this paper, we deal with the problem of the uniqueness of a minimal system of binomial
generators of a semigroup ideal. Concretely, we give different necessary and/or sufficient …

To any toric ideal IA, encoded by an integer matrix A, we associate a matroid structure called
the bouquet graph of A and introduce another toric ideal called the bouquet ideal of A. We …

In this paper, we consider the following question:" given the multiplicity $ m $ and
embedding dimension $ e $ of a numerical semigroup $ S $, what can be said about the …

Let IL, ρ be a lattice ideal. We provide a necessary and sufficient criterion under which a set
of binomials in IL, ρ generates the radical of IL, ρ up to radical. We apply our results to the …

In this paper, we consider the following question:“given the multiplicity m and embedding
dimension e of a numerical semigroup S, what can be said about the cardinality η of a …

We present an explicit minimal set of generators for the defining ideal of the family of
Backelin semigroups and find its Betti numbers. In particular, we compute the type of the …