Vol. 20, No. 2, 1967

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Ideals of the principal class, R-sequences and a certain monoidal transformation

Edward Dewey Davis

Vol. 20 (1967), No. 2, 197–205

We consider the algebra generated over the ring R by the quotients {x1∕x,,xn∕x}. This “monoidal transform” R[x1∕x,,xn∕x] may be regarded as the homomorphic image of the polynomial ring R[Xi,,Xn]. Examination of the kernel of this homomorphism gives in one instance the theorem of analytic independence of systems of parameters and in another the analogous theorem about R-sequences in arbitrary commutative rings. We combine these results with some older work of ours (included in an appendix) to give several characterizations of ideals in Noetherian rings generated by R-sequences.

Mathematical Subject Classification
Primary: 13.20
Secondary: 13.93
Received: 20 January 1966
Published: 1 February 1967
Edward Dewey Davis