5 papers · 1 filter
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…