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Bao Do, a senior mathematics major, and Alin Stancu, a mathematics professor at Columbus State University, recently co-authored a paper titled “Hochschild Extensions of Weekly (nil) Clean Rings, Fine rings and UN-rings” in the Fall 2016 issue of Pi Mu Epsilon Journal, a peer-reviewed mathematics journal.
Inspired by recent developments in Ring Theory, a branch of Abstract Algebra, Do and Stancu’s work presents a new and elementary characterization of the properties of certain algebraic structures, which are called Extensions of Rings. Research on extensions can be viewed as a type of abstract arithmetic, analogous to studying which properties of the addition and multiplication of integers are inherited by fractions. Understanding which results are preserved when one goes from a “local” to a “global” setting is an important theme in many disciplines and Bao and Stancu’s work is a mathematical version of this idea. Namely, their results can be used to determine under what conditions the properties of certain rings are inherited by their extensions.