REDUCTION NUMBERS AND IDEALS OF ANALYTIC SPREAD ONE
Abstract
Let (R,M) be a commutative Noetherian local ring having an infinite residue field and suppose I is an ideal in R. The reduction number of I (denoted r(I)) is defined, and conditions on R which force r(I) (LESSTHEQ) 1 for every regular analytic spread one ideal I of R are obtained. Several examples are given illustrating r(I) and the role it sometimes plays in connection with other concepts. The situation for ideals having analytic spread larger than one is also discussed, and an interpretation of r(I) involving the relations on the generators of I is investigated.
Degree
Ph.D.
Subject Area
Mathematics
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