Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 2610.06426

Reflexive ideals of a numerical semigroup

P. Campochiaro·M. D'Anna·P. A. Garcia-Sanchez
View original source ↗Read source document ↗Export metadata ↓

Abstract

We study the reflexivity property of ideals in numerical semigroups. In particular, we characterize irreducible reflexive ideals and determine the Apéry set of a reflexive ideal. Moreover, we study how reflexivity allows us to characterize some classes of numerical semigroups and the interaction of reflexivity with the property of being a trace ideal.

Explore related subjects

math.AC

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

P. Campochiaro, M. D'Anna, P. A. Garcia-Sanchez. 2026-10-05. Reflexive ideals of a numerical semigroup. https://arxiv.org/abs/2610.06426

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

On the vertex connectivity of weakly zero-divisor graph of commutative rings

The weakly zero-divisor graph $WΓ(R)$ of a commutative ring $R$ is the simple undirected graph whose vertices are nonzero zero-divisors of $R$, and two distinct vertices $x$, $y$ are adjacent if and only if there exists $w\in {\rm ann}(x)$ and $ z\in {\rm ann}(y)$ such that $wz =0$. In this paper, first we prove that the vertex connectivity of $WΓ(R)$ is equal to its minimum degree, where $R$ is either an Artinian ring or reduced ring. For any finite ring $R$, we obtain the vertex connectivity of $WΓ(R)$. Moreover, this paper characterizes all the vertices that attain the minimum degree of $WΓ(R)$.

math.AC↗
arXiv2026

The Coproduct of Ideals and the Coprime Spectrum

We introduce the coproduct of ideals and the notion of coprime ideal, extending the Heyting-algebra perspective on ideal lattices to arbitrary commutative rings. The resulting coprime spectrum is a topological space, defines a covariant functor on CF-morphisms of commutative rings, i.e. morphisms that extend ideals and are coprime faithful, classifies fields among integral domains, and in dual rings is homeomorphic to the prime spectrum. This offers an elementary, lattice-theoretic counterpart to the geometric study of nilpotents.

math.AC↗
arXiv2026

Weak and Serre Lifting of Cyclic Modules and the Liftability of Auslander Transposes

Let $Q$ be a local ring, $f$ a nonzerodivisor, and $R=Q/(f)$. We characterize weak and Serre liftability of cyclic $R$-modules under suitable hypotheses, obtaining complete-intersection criteria for Serre liftability in small height. We prove that the tensor product of two weakly liftable cyclic modules remains weakly liftable when their first Tor module vanishes, and give sufficient conditions for tensor products to preserve Serre liftability. We construct an Artinian Gorenstein quotient $Q/I$, with $Q$ regular, that is perfect over $R$ and Serre liftable but not weakly liftable to $Q$, showing that the negative answer to a question of Jorgensen persists in this more restrictive setting. Finally, we characterize when a lift induces a lift of the Auslander transpose and obtain a freeness criterion related to the Auslander-Reiten conjecture, recovering a theorem of Ghosh and Samanta.

math.AC↗