A Note on GP-Injectivity

New characteristic properties of left GPGV-rings are given. It is shown that if R is a left GPGV-ring, then for any nonzero element a in R, there is a positive integer n such that an≠ 0 and (RaR+ l(an))⊕ L=R for some left ideal L contained in Soc(RR). As a corollary of this result, we are able to give a positive answer to a question raised by Yue Chi Ming.