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Module Structure of Rings of Differential Operators
Author(s) -
Coutinho S. C.,
Holland M. P.
Publication year - 1988
Publication title -
proceedings of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.899
H-Index - 65
eISSN - 1460-244X
pISSN - 0024-6115
DOI - 10.1112/plms/s3-57.3.417
Subject(s) - mathematics , rank (graph theory) , affine transformation , ideal (ethics) , differential operator , ring (chemistry) , pure mathematics , zero (linguistics) , differential (mechanical device) , variety (cybernetics) , field (mathematics) , discrete mathematics , combinatorics , physics , philosophy , chemistry , linguistics , statistics , organic chemistry , epistemology , thermodynamics
Let X be a smooth irreducible affine k ‐variety for k a field of characteristic zero and let D ( X ) denote the ring of k ‐linear differential operators on X . It is shown that every right ideal of D ( X ) is generated by three elements and that stably free D ( X )‐modules of rank at least 3 are free.