251 citations · 388 across the 12 of their papers we have counts for
10 papers · 1 filter
Families of numerical semigroups and a special case of the Huneke-Wiegand conjecture
Miguel Landeros, Christopher O'Neill, Roberto Pelayo +3
The Huneke-Wiegand conjecture is a decades-long open question in commutative algebra. García-Sánchez and Leamer showed that a special case of this conjecture concerning numerical s…
Apéry sets of shifted numerical monoids
Christopher O'Neill, Roberto Pelayo
A numerical monoid is an additive submonoid of the non-negative integers. Given a numerical monoid , consider the family of "shifted" monoids obtained by adding to eac…
Realizable sets of catenary degrees of numerical monoids
Christopher O'Neill, Roberto Pelayo
The catenary degree is an invariant that measures the distance between factorizations of elements within an atomic monoid. In this paper, we classify which finite subsets of $\math…
Minimal presentations of shifted numerical monoids
Rebecca Conaway, Felix Gotti, Jesse Horton +4
A numerical monoid is an additive submonoid of the non-negative integers. Given a numerical monoid , consider the family of "shifted" monoids obtained by adding to eac…
On Delta Sets and their Realizable Subsets in Krull Monoids with Cyclic Class Groups
Scott T. Chapman, Felix Gotti, Roberto Pelayo
Let be a commutative cancellative monoid. The set , which consists of all positive integers which are distances between consecutive factorization lengths of elements in $…
Factorization invariants in numerical monoids
Christopher O'Neill, Roberto Pelayo
Nonunique factorization in commutative monoids is often studied using factorization invariants, which assign to each monoid element a quantity determined by the factorization struc…
On dynamic algorithms for factorization invariants in numerical monoids
Thomas Barron, Christopher O'Neill, Roberto Pelayo
Studying the factorization theory of numerical monoids relies on understanding several important factorization invariants, including length sets, delta sets, and -primality. Whi…
How Do You Measure Primality?
Christopher O'Neill, Roberto Pelayo
In commutative monoids, the -value measures how far an element is from being prime. This invariant, which is important in understanding the factorization theory of monoids, has…
Factorization Properties of Leamer Monoids
Jason Haarmann, Ashlee Kalauli, Aleesha Moran +2
The Huneke-Wiegand conjecture has prompted much recent research in Commutative Algebra. In studying this conjecture for certain classes of rings, García-Sánchez and Leamer construc…
On the Linearity of ω-primality in Numerical Monoids
Christopher O'Neill, Roberto Pelayo
In an atomic, cancellative, commutative monoid, the ω-value measures how far an element is from being prime. In numerical monoids, we show that this invariant exhibits eventual qua…