matrix valuation pseudo ring (mvpr) and an extension theorem of matrix valuation

let r be a ring and v be a matrix valuation on r. it is shown that, there exists a correspondence between matrix valuations on r and some special subsets ?(mvpr) of the set of all square matrices over r, analogous to the correspondence between invariant valuation rings and abelian valuation functions on a division ring. furthermore, based on malcolmson’s localization, an alternative proof for the following result is presented. “there exists a natural bijection between the matrix valuations on r and valuated epic r-fields.”