Prime ideals in commutative rings and atoms

Joint seminar Department of Mathematics_Centro Internazionale per la Ricerca Matematica

Luogo: Dipartimento di Matematica, via Sommarive, 14 - Povo (TN) - Sala Seminari "-1"
Ore: 11:30

Relatore:

• Henrik Holm (University of Copenhagen)

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 some aspects of prime ideals in commutative rings. In the second part, I will explain elements of Kanda's recently developed theory of atoms (in the mathematical sense - not in the sense of physics). 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 briefly explain some joint work with R. H. Bak, on how to actually compute/determine the atoms for certain types of non-commutative rings.

Referente: Sonia Mazzucchi