CONSTRUCTION OF STANDARD BASES OF RIGHT K -LESS-THAN-A-ROOT-MODULES

We define bases Of right sub-K[A]-Modules of K[A]q, for which we give some results. When q=1, the submodules we consider reduce to right ide als of the ring of noncommutative polynomials over A. We first introdu ce the concept of an independent basis of a submodule (with respect to an order on the set of words), of which we give a characterisation in terms of prefix codes. Amongst all the independent bases of M, we sel ect a singular basis which we call the standard basis of M. We give an explicit description of this basis. We show how these bases can, in f act, be calculated when the submodule is of finite type. Our methods e nable working with (right) sub-K[A]-modules of K[A]q and the quotient modules K[A]q/M.