https://hdl.handle.net/10481/43089 2026-04-19T07:11:37Z 2026-04-19T07:11:37Z Moreno Frías, María Ángeles Rosales González, José Carlos https://hdl.handle.net/10481/111941 2026-03-06T12:27:23Z

Odd Right-End Numerical Semigroups Moreno Frías, María Ángeles; Rosales González, José Carlos An odd right-end semigroup (hereinafter Ore semigroup) is a numerical semigroup S verifying that x + 1 ∈ S for every x ∈ S\{0} such that x is even. The introduction and study of these semigroups is the purpose of the present work. In particular, we will give some algorithms which compute all Ore semigroups with a given genus, a fixed Frobenius number and aspecific multiplicity. We will see that if X is a set of positive integers, then there exists the smallest Ore semigroup, under the inclusion sets, that contains X. We will denote this semigroup by θ[X] and present an algorithm to calculate it. Finally, we will study the embedding dimension, the Frobenius number, and the genus of Ore semigroups of the form θ[{m}], where m is a positive integer. As a consequence of this study, we will prove that this kind of semigroup satisfies Wilf’s conjecture.

Gómez-Torrecillas, José Sánchez-Hernández, José Patricio https://hdl.handle.net/10481/111862 2026-03-04T07:42:58Z

Skew Laurent series and general cyclic convolutional codes Gómez-Torrecillas, José; Sánchez-Hernández, José Patricio

Moreno Frías, María Ángeles Rosales González, José Carlos https://hdl.handle.net/10481/110237 2026-01-26T09:11:42Z

Radical Numerical Semigroups Moreno Frías, María Ángeles; Rosales González, José Carlos This work contributes to the study of radical numerical semigroups. If 𝑛� ∈ℤ where 𝑛� ≥2, then the product of all its prime positive divisors is called the radical of n. It is denoted by r⁡(𝑛�). A radical numerical semigroup is a numerical semigroup S such that 𝑠� +r⁡(𝑠�) ∈𝑆� for every 𝑠� ∈𝑆�\{0}. We present three algorithms that will help us understand the structure of radical semigroups. These algorithms allow us to calculate all radical numerical semigroups with a fixed genus, with a fixed Frobenius number, as well as with a fixed multiplicity. Furthermore, given X, a set of positive integers such that gcd⁡(𝑋�) =1, we will prove the existence of the smallest radical semigroup containing X. We will also present an algorithm to obtain it.

Jara Martínez, Pascual Giar Mohamed, Salwa https://hdl.handle.net/10481/108940 2025-12-18T10:32:26Z

Fuzzy and Gradual Prime Ideals Jara Martínez, Pascual; Giar Mohamed, Salwa There is a correspondence between equivalence classes of fuzzy ideals, on a commutative ring, and decreasing gradual ideals. In this paper, we explore how to construct a fuzzy ideal starting from any decreasing gradual ideal σ. To achieve this, we consider an interior operator, σ d , and a closure operator, σ e , and show that the pair (σ d , σ e ) is always an F-pair, which defines a fuzzy ideal. Furthermore, this correspondence, and its inverse, preserves sums, intersections and products. This therefore provides an algebraic framework for studying fuzzy ideals. In particular, prime fuzzy ideals and weakly prime fuzzy ideals have their counterparts in the theory of decreasing gradual ideals, offering us a new perspective on these particular objects. One of the main objectives is to characterize fuzzy prime ideals using single fuzzy elements and gradual ideals.

Aragón, Roberto G. Jara Martínez, Pascual Medina, Jesús https://hdl.handle.net/10481/108865 2025-12-16T12:22:56Z

General and left-continuous operators on lattice-based sums Aragón, Roberto G.; Jara Martínez, Pascual; Medina, Jesús Lattice-based sum provides a procedure to obtain posets and lattices from families of posets and lattices, respectively. Establishing sufficient conditions to ensure the lattice structure was the most significant challenge achieved in previous works. Next steps are to consider structures with general operators defined on the lattices of the family, introduce a sum of these operators on the obtained lattice-based sum and study the properties preserved by this new definition. We will prove that the natural definition preserve, in general, the monotonicity, associativity, commutativity, etc. This paper also introduces a new mechanism focused on preserving the left-continuity property of the operators defined on the lattices. This new approach also preserves the associativity and the infimum of non-empty subsets, and takes into account (infinite) complete lattices, unlike the previous works.