2015/07/16 by Kashcheyeva, Olga
#13A18 #13H99 #Commutative Algebra (math.AC) #FOS: Mathematics
paper · doi:10.48550/arxiv.1507.04669
We work with rational rank 1 valuations centered in regular local rings. Given an algebraic function field K of transcendence degree 3 over k, a regular local ring R with QF(R)=K and a k-valuation ν of K, we provide an algorithm for constructing a generating sequences for ν in R. We then develop a method for determining a valuation ν on k(x,y,z) through the sequence of defining values. Using the above results we construct examples of valuations centered in k[x,y,z](x,y,z) and investigate their semigroups of values.