8 citations · 12 across the 10 of their papers we have counts for
9 papers · 1 filter
On the subatomicity of polynomial semidomains
Felix Gotti, Harold Polo
A semidomain is an additive submonoid of an integral domain that is closed under multiplication and contains the identity element. Although atomicity and divisibility in integral d…
Arithmetic of additively reduced monoid semidomains
Scott T. Chapman, Harold Polo
A subset of an integral domain is called a semidomain if the pairs and are semigroups with identities; additionally, we say that is additively redu…
On the arithmetic of polynomial semidomains
Felix Gotti, Harold Polo
A subset of an integral domain is called a semidomain provided that the pairs and are semigroups with identities. The study of factorizations in integr…
A characterization of finite factorization positive monoids
Harold Polo
We provide a characterization of the positive monoids (i.e., additive submonoids of the nonnegative real numbers) that satisfy the finite factorization property. As a result, we es…
On the factorization invariants of the additive structure of exponential Puiseux semirings
Harold Polo
Exponential Puiseux semirings are additive submonoids of $\qq_{\geq 0}$ generated by almost all of the nonnegative powers of a positive rational number, and they are natural genera…
Approximating length-based invariants in atomic Puiseux monoids
Harold Polo
A numerical monoid is a cofinite additive submonoid of the nonnegative integers, while a Puiseux monoid is an additive submonoid of the nonnegative cone of the rational numbers. Us…
On the atomic structure of exponential Puiseux monoids and semirings
Sofía Albizu-Campos, Juliet Bringas, Harold Polo
A Puiseux monoid is an additive submonoid of the nonnegative cone of the rational numbers. We say that a Puiseux monoid is exponential provided that there exist a positive rati…
On the sets of lengths of Puiseux monoids generated by multiple geometric sequences
Harold Polo
In this paper, we study some of the factorization aspects of rational multicyclic monoids, that is, additive submonoids of the nonnegative rational numbers generated by multiple ge…
On three families of dense Puiseux monoids
Scott. T. Chapman, Felix Gotti, Marly Gotti +1
A positive monoid is a submonoid of the nonnegative cone of a linearly ordered abelian group. The positive monoids of rank are called Puiseux monoids, and their atomicity, arit…