… over more general local rings. However, we only treat the case of curves over discrete
valuation rings (DVRs) here, as it seems sufficiently interesting and already sufficiently involved. …

… of modules with Krull dimension over general valuation rings to those over valuation domains
… Totally branched and discrete valuation domains appeared under other names such as ‘…

… Local rings are not assumed Noetherian, and fields are considered to be discrete valuation
rings, … By the dimension of a ring, we always mean its Krull dimension. In a quotient R/I of a …

… Instead of Zp, we will work more generally with any complete discrete valuation ring (DVR)
R with the maximal ideal m, or simply denoted as .R;m/, whose residue field R=m is finite so …

… valuation ring, a pseudo-valuation ring and a pseudo-almost valuation ring between a
commutative ring A and A ⋉ E (the trivial ring extension of A arising from an A-module E). Also, we …

… , the results of this section hold over any complete discrete valuation ring \({\mathcal {O}}\)
with residue field \(k={\bar{{\mathbb {F}}}}_p\), but we have in mind the ring of Witt vectors of k. …

… We also show that if A is a graded ring and E a nonzero graded A-module. … ring is a gr-valuation
ring if ond only if A is a gr-valuation domain, E is a gr-divisible and gr-uniserial A-module…

… study of modules over valuation rings. Over a valuation ring, uniserial modules play a …
A discrete valuation of a monoid M is a nonzero monoid homomorphism v: M → N0. Here …

… valued field. We reinterpret some results of MacLane and Vaquié on extensions of v to valuations
on the polynomial ring … mixture of ordinary and limit augmentations of valuations. Every …

… In light of Lemma 3.3, we can prove Theorem 3.5 by means of relating modules over the
monad γ∗γ∗ with modules over the motivic spectrum γ∗γ∗(1S). Thus, given S ∈ S our task is to …