Global Dimension of Differential Operator Rings. III | Zendy

Goodearl K. R. | Zendy

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Global Dimension of Differential Operator Rings. III

Author(s) -

Goodearl K. R.

Publication year - 1978

Publication title -

journal of the london mathematical society

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.441

H-Index - 62

eISSN - 1469-7750

pISSN - 0024-6107

DOI - 10.1112/jlms/s2-17.3.397

Subject(s) - global dimension , mathematics , dimension (graph theory) , abelian group , dimension theory (algebra) , commutative property , pure mathematics , noetherian ring , noetherian , krull dimension , differential operator , ring (chemistry) , algebra over a field , chemistry , organic chemistry

The aim of this paper is to derive formulas for the global homological dimension of the ring R [θ 1 ,..,θ u ] of formal linear differential operators over a commutative noetherian ring R with u commuting derivations. Since the case when R has finite global dimension has been completed in [3], the present paper deals mainly with the case when R has infinite global dimension. Formulas are derived which show exactly when R [θ 1 ,.. θ u ] has finite global dimension, and what the value of that dimension is. Examples are constructed of commutative noetherian domains R such that R is torsion‐free as an abelian group, R has infinite global dimension, and R has a derivation such that R [θ] has finite global dimension.

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