Projective star operations on polynomial rings over a field

摘要

We consider the polynomial ring S:= K[X_0, ...,X_n] over a field K and the rings Ri:= K[(_(X0)/X_i), ..., (X_n/X_i)] for 0≤i≤n. We introduce the notion of a projective star operation on S and relate it to the classical star operations on the R_i's. We show that the projective Kronecker function ring PKr (S, *) of S is the intersection of the Kronecker function rings Kr (R_i, *_i), 0≤i≤n, where the *i's are pairwise compatible e.a.b. star operations on the Ri's and * is a projective star operation on S built from the *i's.