The Closed-Point Zariski Topology for Irreducible Representations

Details The Closed-Point Zariski Topology for Irreducible Representations The Closed-Point Zariski Topology for Irreducible Representations

2005-07-27

arxiv.org/abs/math/0507551v1

Mathematics

Rings and Algebras

10 pages; AMS-TeX

Scientific paper

In previous work, the second author introduced a topology, for spaces of irreducible representations, that reduces to the classical Zariski topology over commutative rings but provides a proper refinement in various noncommutative settings. In this paper, a concise and elementary description of this refined Zariski topology is presented, under certain hypotheses, for the space of simple left modules over a ring R. Namely, if R is left noetherian (or satisfies the ascending chain condition for semiprimitive ideals), and if R is either a countable dimensional algebra (over a field) or a ring whose (Gabriel-Rentschler) Krull dimension is a countable ordinal, then each closed set of the refined Zariski topology is the union of a finite set with a Zariski closed set. The approach requires certain auxiliary results guaranteeing embeddings of factor rings into direct products of simple modules. Analysis of these embeddings mimics earlier work of the first author and Zimmermann-Huisgen on products of torsion modules.

Affiliated with

Also associated with

No associations

Rating

The Closed-Point Zariski Topology for Irreducible Representations does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with The Closed-Point Zariski Topology for Irreducible Representations, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The Closed-Point Zariski Topology for Irreducible Representations will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-494906