Polynomes de ore, series formelles tordues et anneaux filters complets herediataires

Abstract

The Ore extension A [t ; τ, δ] of a semi-simple artinian ring A ,with , is right hereditary, even if the ring monomorphism τ is not surj ective (th . 2.1) . If δ = 0, then R is the associated graded ring of the skew power series ring , so we are led to study fil tered modules over a complete filtered ring A , with decreasing filtrations, which are projective, with respect of a certain family of epimorphisms , in the category of filtered A-modules, which we call f-projective (§§3,4). The skew power series ring over a semisimple artinian ring is right f-hereditary, i.e. every right ideal is f-projective (th. 4.5).