Vol. 60, No. 2, 1975

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ISSN: 0030-8730
On Rees localities and Hi-local rings

Louis Jackson Ratliff, Jr.

Vol. 60 (1975), No. 2, 169–194

The main theorem gives a necessary and sufficient condition for each Rees locality = R[tb,u](M,tb,u) of a local ring (R,M) with respect to a principal ideal bR in R to be either an Hi-ring (that is, for all prime ideals p in such that height p = i, depth p = altitude ℒ− i) or a homogeneously Hi-ring (same condition holds for homogeneous p). Numerous corollaries follow concerning the cases: R is complete; R is Henselian; and, is Hi, for all i 0. A generalization to ideals generated by more than one element is given, and we relate the results to two of the chain conjectures on prime ideals.

Mathematical Subject Classification 2000
Primary: 13H10
Received: 16 October 1974
Published: 1 October 1975
Louis Jackson Ratliff, Jr.