… For valuations of arbitrary rank, different approaches to this problem were developed by …
polynomials appear as a new feature. Starting with a valuation µ0 which admits key polynomials …

… a valuation on FLxJ by means of the valuations … We will compute the valuations on Q[x]
whose value monoids are groups and whose residue class rings are locally finite fields (ie are …

… polynomials rings.) The aim of this paper is to study real valuations on skew polynomials
rings… = R ∪ {∞} satisfying the standard axioms of valuations, whose restriction to D is non-trivial …

… a polynomial ring over K in two indeterminates. As our purpose is a study of the f-ideals in ©
belonging to valuations v of 2 over K, these valuations … Valuation ideals in a ring with chain …

… ū, , ; let ū, = ū and u, = u; we take in the polynomial ring Kļū] a maximal ideal A which is
not ramified in the integral closure of Kū] in the field T = K(ū, b); (hence A is also …

… of a Krull ring S such that RQ is a valuation ring for every finite index Q = P ∩ R, P in Spec1(S),
we construct polynomials that map R into the maximal possible (for a monic polynomial of …

… We shallshowthata setofalldescendedvaluations ofa valuation of K[x]ispartiallylinearlyordered,
whilea setofalldescendedvaluationsof … V10 of K[x] is defined as follows, for any polynomial …

… for completeness with considerations on valuations of a polynomial ring of one variable. …
Now we consider valuations of polynomial rings of two variables. A valuation of a ring R can be …

… for rational functions we single out in F the ring C[a:] of polynomials in 2. Suppose the … We
shall be dealing with polynomials f(t) in the polynomial ring O[t]. Hensel’s criterion shows how …

… valuations on an integral domain R to the ring of polynomials R f x], where xis transcendental
over R • MacLane*s results are based on the assumption that all valuations … the valuations …