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Journal of the London Mathematical Society 2001 63(2):319-335; doi:10.1017/S0024610700001927
© 2001 by London Mathematical Society
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© The London Mathematical Society

Finite Modules of Finite Injective Dimension Over a Noetherian Algebra

Shiro Goto and Kenji Nishida

Department of Mathematics, School of Science and Technology, Meiji University Kawasaki 214-8571, Japan, goto{at}math.meiji.ac.jp
Department of Mathematical Sciences, Shinshu University Matsumoto 390–8621, Japan, kenisida{at}math.shinshu-u.ac.jp

Received 22 November 1999. Revision received 5 June 2000.

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.


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