2025/06/30 by Moles, Grant · 1 citation
#Commutative Algebra (math.AC) #FOS: Mathematics
paper · doi:10.48550/arxiv.2506.24031
When studying the properties of a ring R, it is often useful to compare R to other rings whose properties are already known. In this paper, we define three ways in which a subring R might be compared to a larger ring T: being associated, being ideal-preserving, or being locally associated. We then explore how these properties of a subring might be leveraged to give information about R, including applications to the field of factorization. Of particular interest is the result that an order in a number field is associated if and only if it is both ideal-preserving and locally associated. We conclude with a discussion of how these properties are realized in the case of orders in a number field and how such orders might be found.