The algebraic structure of the get of all proper rational vectors contained in a given rational vector space𝒯(s)is shown to be that of a noothorian ℝpr(s) -motiulo M*. ( Ropf;pr(a) is the ring ofproperrational functions.) The proper submodulesMtofM*form an ascending chain of submodules partially ordered by an invariant ofMtdefined as the valuation ats= ∞ ofMt, Tho various bases ofMtare examined and classified according to their property of ‘column reduceness at s = ∞’The concept of aprime column reduced at basis ofMtis introduced. It is shown that tho prime bases ofMtcan be further classified by their MacMillan degrees and the existence of minimal MacMillan degree bases forMtis established. A prime and minimal MacMillan degree basis ofMtextends Forney's concept of a minimal polynomial basis of∞ (s)for the RprMt-module The MacMillan degrees of the columns of such bases form a set of invariants Mtfor which are defined as the𝒯(s)generalized invariant dynamicol indices ofMtand a simple relation is established between (I) the generalized invariant dynamical indicesMt(ii) the orders of zeros at= ∞ sand (iii) the Forney invariant dynamical indices of Finally those results are specialized to the (maximal) noetherian ( Rpr(a)smodule M* it is shown that in this case the ' generalized invariant dynamical indices ' of M*. coincide with the invariant dynamical indices of Forney for𝒯(s)thus providing an alternative interpretation of the Forney ' invariant dynamical order ' of𝒯(s)as an absolute minimum of the MacMillan degree of any proper basis for𝒯(s)