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6 papers · 1 filter
Growth of rank 1 valuation semigroups
Steven Dale Cutkosky, Kia Dalili, Olga Kashcheyeva
We consider the question of which semigroups can occur as the semigroup of positive values of a rank 1 valuation dominating a Noetherian local ring . We give a number o…
Toroidalization of generating sequences in dimension two function fields of positive characteristic
Laura Ghezzi, Olga Kashcheyeva
We give a characteristic free proof of the main result of our previous paper (math.AC/0509697) concerning toroidalization of generating sequences of valuations in dimension two fun…
Algebraic series and valuation rings over nonclosed fields
Steven Dale Cutkosky, Olga Kashcheyeva
Suppose that is an arbitrary field. Consider the field , which is the quotient field of the ring of formal power series in the variables $x…
Canonical Characteristic Sets of Characterizable Differential Ideals
Oleg Golubitsky, Marina Kondratieva, Alexey Ovchinnikov
We study the concept of canonical characteristic set of a characterizable differential ideal. We propose an efficient algorithm that transforms any characteristic set into the cano…
Lefschetz extensions, tight closure, and big Cohen-Macaulay algebras
Matthias Aschenbrenner, Hans Schoutens
We associate to every equicharacteristic zero Noetherian local ring a faithfully flat ring extension which is an ultraproduct of rings of various prime characteristics, in a we…
Bounds and definability in polynomial rings
Matthias Aschenbrenner
We study questions around the existence of bounds and the dependence on parameters for linear-algebraic problems in polynomial rings over rings of an arithmetic flavor.In particula…