Prime ideals in commutative rings and atoms
Università degli Studi Trento
38123 Povo (TN)
Tel +39 04 61/281508-1625-1701-3898-1980.
dept.math [at] unitn.it
Joint seminar Department of Mathematics_Centro Internazionale per la Ricerca Matematica
Venue: Dipartimento di Matematica, via Sommarive, 14 - Povo (TN) - Sala Seminari "-1"
At: 11:30
Speaker:
- 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.
Contact Person: Sonia Mazzucchi