… Consequently, if R is a valuation domain each P -flat module is finitely projective. When R
is a valuation ring, we prove that this result holds if and only if the ring Q of quotients of R is …

… By a valuation ring R will be meant a commutative ring with 1 whose ideals are totally …
rings are not fields. It is obvious that factor rings of valuation rings are again valuation rings. …

… Finally, we discuss the case where the base ring is a discrete valuation ring (abbr. dvr).
Suppose A is a dvr with maximal ideal m (we do not need to assume A be complete), and let R ž …

… , modules over the localization ℤp of the ring ℤ with respect to the ideal generated by the prime
integer p). The ring … for modules over arbitrary discrete valuation domains. In the theory of …

… -injective modules. We extend this last result to every valuation ring R by replacing S with
the pure-injective hull R ̂ of R . As in the domain case, R ̂ is a faithfully flat module. Moreover…

… rise to valuation rings Av of the field of quotients of /i, such that Av ^ R. Every flat valuation is
… on /?, satisfying condition (0) and the valuations v of K such that Αυ sA9 . To each length A, …

… Then we prove the existence and uniqueness of minimal models over a discrete valuation
ring, in the case when the genus of the generic fiber is greater than zero. (Otherwise, we have …

… of direct products of division rings and all commutative regular rings) are distributive; all
valuation rings in division rings and all commutative Dedekind rings (eg, rings of integral …

… by inclusion and a ring R is a valuation ring if it is uniserial as R-module. Recall that
every finitely presented module over a valuation ring is a finite direct sum of cyclic modules [18, …

… Let A be a ring, an A-module E is said to be uniserial if the set … ring A is called a valuation
ring if A is an uniserial A-module. We note that A is a valuation ring if and only if A is a local ring …