Group actions and rational ideals

Details Group actions and rational ideals Group actions and rational ideals

2008-01-22

arxiv.org/abs/0801.3472v3

Algebra and Number Theory 2 (2008), 467-499

Mathematics

Rings and Algebras

21 pages; numbering aligned with published version (ANT)

Scientific paper

We develop the theory of rational ideals for arbitrary associative algebras R without assuming the standard finiteness conditions, noetherianness or the Goldie property. The Amitsur-Martindale ring of quotients replaces the classical ring of quotients which underlies the previous definition of rational ideals but is not available in a general setting. Our main result concerns rational actions of an affine algebraic group G on R. Working over an algebraically closed base field, we prove an existence and uniqueness result for generic rational ideals: for every G-rational ideal I of R, the closed subset of the rational spectrum Rat R that is defined by I is the closure of a unique G-orbit in Rat R. Under additional Goldie hypotheses, this was established earlier by Moeglin and Rentschler (in characteristic zero) and by Vonessen (in arbitrary characteristic), answering a question of Dixmier.

Affiliated with

Also associated with

No associations

Rating

Group actions and rational ideals 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 Group actions and rational ideals, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Group actions and rational ideals will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-182984