Relative Semi-hereditary Rings and Semi-hereditary Rings

  title={Relative Semi-hereditary Rings and Semi-hereditary Rings},
  author={Ban Xiu-he},
Using coflat modules and M-semi-hereditary rings, it is obtained that R is a semi- hereditary ring iff the factors of E(R) is coflat iff R is a R-semi-hereditary ring iff the sum of two injective submodules in a module that are isomorphic is coflat.Then, by coflat modules the following results are shown: R is a QF- ring iff coflat modules are projective iff projective modules are coflat and R is a Noetherian ring;R is a regular ring iff every cyclic left ideal in R is coflat.