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Finite Modules of Finite Injective Dimension Over a Noetherian Algebra
Author(s) -
Goto Shiro,
Nishida Kenji
Publication year - 2001
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 - 10.1017/s0024610700001927
Subject(s) - mathematics , injective function , injective module , noetherian , pure mathematics , local ring , dimension (graph theory) , equivalence (formal languages) , noetherian ring , commutative property , global dimension , krull dimension , commutative ring , discrete mathematics , algebra over a field , ring (chemistry) , chemistry , organic chemistry
Let R be a commutative Noetherian ring. Let P( R ) (respectively, I( R )) be the category of all finite R ‐modules of finite projective (respectively, injective) dimension. Sharp [ 9 ] constructed a category equivalence between I( R ) and P(R) for certain Cohen–Macaulay local rings R . Thus many properties about finite modules of finite projective dimension can be connected with those of finite injective dimension through this equivalence.