Factorizations of Birational Extensions of Local Rings Steven Dale Cutkosky and Hema Srinivasan
نویسنده
چکیده
for 1 ≤ i ≤ m. Suppose that P ⊂ R is a regular prime (R/P is a regular local ring) and 0 6= f ∈ P . The regular local ring R1 = R[ P f ]m where m is a maximal ideal of R[ P f ] containing mR is called a monoidal transform of R. Suppose that V is a valuation ring of the quotient field of S which dominates S (and thus dominates R). Then given a regular prime P of R (or of S) there exists a unique monoidal transform R1 of R (or S1 of S) obtained from P such that V dominates R1 (or V dominates S1). The local monomialization theorem of [C2] and [C4] shows that given an extension R → S ⊂ V as above such that R,S are essentially of finite type over a field k of characteristic zero, there exists a commutative diagram
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