Preliminaries Algebraic Situation

All rings R will be unital and all modules X will be right modules. I a basis for an R-module X is a R-linearly independent generating set. I An R-module X has dimension if I it admits a finite basis, and I all finite bases of X have the same cardinality. I A ring R has Invariant Basis Number if the free R-modules Rn all have dimension. I A ring R is dimensional if all R-modules with finite basis have dimension. Examples: Commutative, right-Noetherian, and division rings are dimensional.The rin