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Noetherian Rings with Big Indecomposable Projective Modules
Author(s) -
Hodges T. J.,
Stafford J. T.
Publication year - 1989
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/blms/21.3.249
Subject(s) - krull dimension , mathematics , indecomposable module , noetherian , global dimension , projective module , pure mathematics , finitely generated abelian group , dimension (graph theory) , local ring , noetherian ring , module , ring (chemistry) , projective test , discrete mathematics , regular local ring , algebra over a field , chemistry , organic chemistry
Let { s 1 : 1 ⩽ i < ∞} be a set of strictly positive integers. We produce an example of a ring R such that (a) R is a Noetherian domain, integral over its centre, of (classical or Rentschler‐Gabriel) Krull dimension one and (b) for each i there exists an indecomposable, finitely generated, projective right R ‐module P 1 such that P 1 has uniform dimension s 1 . This answers [3, Question B].