# Henrik Holm

Prime ideals in commutative and non-commutative rings

Date: 3/9/2018

Time: 4:00PM-5:00PM

Place: 315 Armstrong Hall

Abstract:Prime ideals are important in commutative algebra (e.g. localization and Krull dimension), in algebraic geometry (e.g. affine schemes),

and in number theory (e.g factorization in Dedekind domains). This talk --which is about prime ideals, their generalizations, and their

uses -- has three parts: In the first part, I will talk about certain aspects of prime ideals in commutative rings. In the second part, I will explain

elements of Kanda's recently developed theory of (so-called) atoms. The notion of atoms is a useful and interesting generalization of prime ideals

to non-commutative rings (and to abelian categories). In the third part, I will explain work in progress, joint with R. H. Bak, on how to actually

compute/determine the atoms for certain types of non-commutative rings.

All are welcome.