Group actions and rational ideals
| dc.creator | Lorenz, Martin | |
| dc.date | 2008-01-22 | |
| dc.date | 2009-03-16 | |
| dc.date.accessioned | 2026-07-07T12:52:11Z | |
| dc.date.available | 2026-07-07T12:52:11Z | |
| dc.description | 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. | |
| dc.description | 21 pages; numbering aligned with published version (ANT) | |
| dc.identifier | https://arxiv.org/abs/0801.3472 | |
| dc.identifier | http://arxiv.org/abs/0801.3472 | |
| dc.identifier | Algebra and Number Theory 2 (2008), 467-499 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/223221 | |
| dc.subject | Rings and Algebras | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 16W22, 16W35, 17B35 (Primary) | |
| dc.title | Group actions and rational ideals | |
| dc.type | text |