Polynomial rings and H_i-local rings

Louis Jackson Ratliff, Jr.

Vol. 75 (1978), No. 2, 497–510

DOI: 10.2140/pjm.1978.75.497

Abstract

Three theorems concerning when certain localities L of R[X₁,⋯,X_k] are H_i-local rings (that is, for every height i prime ideal p in L, depth p = altitude L − i) are proved, where R is a local ring. A number of known corollaries, as well as some new ones, easily follow.

Mathematical Subject Classification 2000

Primary: 13H05

Secondary: 13F20

Milestones

Received: 22 October 1974

Published: 1 April 1978