4 papers
(Locally) Associated Subrings in Polynomial and Power Series Extensions
Grant Moles, Joseph Swanson
The associated, ideal-preserving, and locally associated properties of subrings, first formally defined in 2024, give a way of understanding the multiplicative structure of a subri…
Locally Associated Orders in Real Quadratic Number Fields
Grant Moles, Talha Khan
In 2025, the concept of an order in a number field being associated, ideal-preserving, or locally associated was introduced in order to tackle problems in factorization. In this pa…
Multiplicative Relationships of Subrings and their Applications to Factorization
Grant Moles
When studying the properties of a ring , it is often useful to compare to other rings whose properties are already known. In this paper, we define three ways in which a subr…
Non-Abelian extensions of degree and in characteristic
Grant Moles
This paper describes in terms of Artin-Schreier equations field extensions whose Galois group is isomorphic to any of the four non-cyclic groups of order or the ten non-Abeli…