8 citations · 9 across the 13 of their papers we have counts for
16 papers
Galois Action and Localization in Number Fields
Jim Coykendall, Jared Kettinger
For a Galois number field , the Galois group acts on the class group in a very natural way: for any $σ\in \text{Gal}(…
On the axioms for a unique factorization domain
Scott T. Chapman, Jim Coykendall
With the growing evolution of the theory of non-unique factorization in integral domains and monoids, the study of several variations to the classical unique factorization domain (…
Elasticity in orders of an algebraic number field with radical conductor ideal and their rings of formal power series
James Barker Coykendall, Grant Moles
Orders in an algebraic number field form a class of rings which are of special historical interest to the field of factorization theory. One of the primary tools used to study fact…
Overrings of half-factorial orders
Jason Boynton, Jim Coykendall, Grant Moles +1
The behavior of factorization properties in various ring extensions is a central theme in commutative algebra. Classically, the UFDs are (completely) integrally closed and tend to…
Norms, Normsets, and Factorization
Jim Coykendall, Richard Erwin Hasenauer
We present a development of norms and discuss their relationship to factorization. In earlier work, the first named author introduced the notion of a normset, which is the image of…
Atomicity in integral domains
Jim Coykendall, Felix Gotti
In algebra, atomicity is the study of divisibility by and factorizations into atoms (also called irreducibles). In one side of the spectrum of atomicity we find the antimatter alge…
Square-difference factor absorbing ideals of a commutative ring
David F. Anderson, Ayman Badawi, Jim Coykendall
Let be a commutative ring with . A proper ideal of is a {\it square-difference factor absorbing ideal} (sdf-absorbing ideal) of if whenever $a^2 - b^2 \in…
Adjacency-Like Conditions and Induced Ideal Graphs
Saba al-Kaseasbeh, Jim Coykendall
In this paper we examine some natural ideal conditions and show how graphs can be defined that give a visualization of these conditions. We examine the interplay between the multip…
Rings of very strong finite type
Jim Coykendall, Tridib Dutta
The SFT (for strong finite type) condition was introduced by J. Arnold in the context of studying the condition for formal power series rings to have finite Krull dimension. In the…
GLocal: Global Graph Reasoning and Local Structure Transfer for Person Image Generation
Liyuan Ma, Kejie Huang, Dongxu Wei +1
In this paper, we focus on person image generation, namely, generating person image under various conditions, e.g., corrupted texture or different pose. To address texture occlusio…
Length-factoriality in commutative monoids and integral domains
Scott T. Chapman, Jim Coykendall, Felix Gotti +1
An atomic monoid is called a length-factorial monoid (or an other-half-factorial monoid) if for each non-invertible element no two distinct factorizations of have…
On the atomicity of monoid algebras
Jim Coykendall, Felix Gotti
Let be a commutative cancellative monoid, and let be an integral domain. The question of whether the monoid ring is atomic provided that both and are atomi…
Spontaneous atomicity for polynomial rings with zero-divisors
Jim Coykendall, Stacy Trentham
In this paper, we show that it is possible for a commutative ring with identity to be non-atomic (that is, there exist non-zero nonunits that cannot be factored into irreducibles)…
On the graph of divisibility of an integral domain
Jason Greene Boynton, Jim Coykendall
It is well-known that the factorization properties of a domain are reflected in the structure of its group of divisibility. The main theme of this paper is to introduce a topologic…
Elasticity in polynomial-type extensions
Mark Batell, Jim Coykendall
The elasticity of an atomic integral domain is, in some sense, a measure of how far the domain is from being a unique factorization domain (or, more properly, a half-factorial doma…
A Homological Approach to Factorization
Jim Coykendall, Brandon Goodell
Mott noted a one-to-one correspondence between saturated multiplicatively closed subsets of a domain D and directed convex subgroups of the group of divisibility D. With this, we c…