We generalize the well-known fact that for a pair of Morita equivalent ringsR andS their maximal rings of quotients are again Morita equivalent: If τn (M) denotes the torsion theory cogenerated by the direct sum of the firstn+1 injective modules forming part of the minimal injective resolution ofM then ατn (R)=τn (S) where α is the category equivalenceR-Mod→S-Mod. Consequently the localized ringsRτn(R) andSτn(S) are Morita equivalent.
We first tackle certain basic questions concerning the Invariant Basis Number (IBN) property and the universal stably finite
factor ring of a direct product of a family of rings. We then consider formal triangular matrix rings and obtain information
concerning IBN, rank condition, stable finiteness and strong rank condition of such rings. Finally it is shown that being
stably finite is a Morita invariant property.