A partition of the set of unary positive primitive (pp) formulas for modules over an associative ring into four regions will be presented. These four types of formula have a bearing on various structural properties of modules, a few instances of which will be discussed in the talk. Domains, specifically Ore domains, turn out to play a prominent role.
One of the four types of formula are called high. These are used to define Ulm submodules and Ulm length of modules over an arbitrary associative ring. Pure injective modules turn out to have Ulm length at most 1 (just as in abelian groups). As a consequence, pure injective modules over RD domains (in particular, pure injective modules over the first Weyl algebra over a field of characteristic 0) decompose into a largest injective and a reduced submodule.
High and low formulas
CANCELED Tue, Oct. 5
Jess Ellis Hagman (Colorado State University)
In this talk I will share my current research that addresses student success in STEM from a critical perspective. A critical perspective on student success means locating student challenges in STEM not within the students' themselves but within the systems at play, and that these systems are failing students not because they are broken but because they are functioning perfectly well based on their design. I will share my research teams' current work focused on student experiences in college precalculus and calculus from a critical perspective, discussing both recent qualitative research and quantitative research studies. I care about these courses personally because I think the content is fun, but more importantly because of the role they play in STEM students' college experiences. This talk is intended for a broad audience to gain a new perspective on student success in STEM and learn a bit about research coming from this perspective.
Speaker bio: Jess Ellis Hagman is an Associate Professor in the Department of Mathematics at CSU. She completed her PhD in Mathematics Education from the joint program between San Diego State University and the University of California, San Diego. Her area of research is undergraduate mathematics education. Her work is focused on dramatically increasing the number and diversity of people who succeed in undergraduate mathematics-especially introductory mathematics courses that often function as a roadblock for STEM intending students. Her current research includes studying characteristics of successful precalculus and calculus programs, focusing on investigating ways departments can create diverse, equitable, and inclusive introductory mathematics programs.