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Projectives of Large Uniform‐Rank, in Krull Dimension 1
Author(s) -
Levy Lawrence S.
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/21.1.57
Subject(s) - mathematics , krull dimension , indecomposable module , global dimension , noetherian , uniqueness , pure mathematics , valuation ring , domain (mathematical analysis) , rank (graph theory) , dimension (graph theory) , regular local ring , noetherian ring , integer (computer science) , discrete mathematics , algebra over a field , field (mathematics) , combinatorics , commutative property , mathematical analysis , computer science , programming language
It is shown that for every positive integer r there is a (left and right) noetherian domain, of Krull dimension 1, that has an indecomposable projective module of uniform‐rank r . Direct‐sum decompositions of free modules over this domain need not satisfy uniqueness of the number of indecomposable summands. If desired, the domain can be taken to be an order over a discrete valuation ring, in a finite‐dimensional division algebra over a global field.