On bordering of regular matrices

AbstractNecessary and sufficient conditions are given for a commutative ring R to be a ring over which every regular matrix can be completed to an invertible matrix of a particular size by bordering. Such rings are precisely the projective free rings. Also, over such rings every regular matrix has a rank factorization. Using the bordering technique, we give an interesting method of computing minors of a reflexive g-inverseG of a regular matrix A when I − AG and I − GA have rank factorizations