Juan Ignacio García-García

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A one-to-one correspondence is described between the setS(m) of numerical semigroups with multiplicity m and the set of non-negative integer solutions of a system of linear Diophantine inequalities. This correspondence infers in S(m) a semigroup structure and the resulting semigroup is isomorphic to a subsemigroup of Nm−1. Finally, this result is(More)
We give an algorithmic method for computing a presentation of any finitely generated submonoid of a finitely generated commutative monoid. We use this method also for calculating the intersection of two congruences on Np and for deciding whether or not a given finitely generated commutative monoid is t-torsion free and/or separative. The last section is(More)
Ideal extensions of semigroups were introduced by Clifford in [1] and since then they have been widely studied (see for instance [2]). Our aim here is to characterize commutative ideal extensions of Abelian groups. We show that they are those commutative semigroups with an idempotent Archimedean element, or equivalently, those commutative semigroups E such(More)
We give a characterization of primary ideals of finitely generated commutative monoids and in the case of finitely generated cancellative monoids we give an algorithmic method for deciding if an ideal is primary or not. Finally we give some properties of primary elements of a cancellative monoid and an algorithmic method for determining the primary elements(More)
Let S be a reduced commutative cancellative atomic monoid. If s is a nonzero element of S, then we explore problems related to the computation of η(s), which represents the number of distinct irreducible factorizations of s ∈ S. In particular, if S is a saturated submonoid of Nd , then we provide an algorithm for computing the positive integer r(s) for(More)
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