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Reflexive modules over regular local rings

โœ Scribed by M. I. Jinnah


Book ID
112500818
Publisher
Springer
Year
1975
Tongue
English
Weight
228 KB
Volume
26
Category
Article
ISSN
0003-889X

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We show that the following two conditions, for each integer r G 1, are equivalent for a finitely generated module M over a complete Noetherian local ring ลฝ . R, แ’Š : embeddable in E r , where E denotes the injective hull of the residue field Rrแ’Š. ลฝ . r ลฝ . b Either M ; E , or else dim Hom Rrแ’Š, M s k

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Let R, m, K be a regular local ring of dimension n and let M be a finite length module over R. This paper gives an affirmative answer to Horrocks' questions when m 2 M s 0, that is, in this case the rank of the ith syzygy of M is at and the ith Betti number of M is at least .