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SCr Modules over Local Rings

✍ Scribed by Jee Heub Koh

Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
134 KB
Volume
239
Category
Article
ISSN
0021-8693

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✦ Synopsis

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 Ε½ . R, α’Š :

embeddable in E r , where E denotes the injective hull of the residue field Rrα’Š. Ε½ . r Ε½ . b Either M ; E , or else dim Hom Rrα’Š, M s kr and there is no R r α’Š R Ε½ . ry kq1 prime ideal ᒍ such that dim Rrᒍ s 1 and Rrᒍ is embeddable in M.

Ž This is an extension of a result of M. Hochster 1977, Trans. Amer. Math. Soc. 231, . 463᎐488 , which is the case r s 1. We show other results related to these conditions.

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