  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.
