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Envelopes and Covers by Modules of Finite Injective and Projective Dimensions

✍ Scribed by S.Tempest Aldrich; Edgar E. Enochs; Overtoun M.G. Jenda; Luis Oyonarte

Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
115 KB
Volume
242
Category
Article
ISSN
0021-8693

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✦ Synopsis

In this paper, we study the existence of βŠ₯ -envelopes, -envelopes, βŠ₯ -envelopes, -covers, and -covers where and denote the classes of modules of injective and projective dimension less than or equal to a natural number n, respectively. We prove that over any ring R, special βŠ₯ -preenvelopes and special -precovers always exist. If the ring is noetherian, the same holds for βŠ₯ -envelopes, and for βŠ₯ -envelopes and -covers when the ring is perfect. When inj.dim R ≀ n then -covers exist, and if R is such that a given class of homomorphisms is closed under well ordered direct limits then -envelopes exist.

πŸ“œ SIMILAR VOLUMES

Finite Length and Pure-Injective Modules
Finite Length and Pure-Injective Modules over a Ring of Differential Operators
✍ Gennadi Puninski πŸ“‚ Article πŸ“… 2000 πŸ› Elsevier Science 🌐 English βš– 123 KB

ww xx Let k be an algebraically closed field of characteristic zero, O O s k x , . . . , x n 1 n the ring of formal power series over k, and D D the ring of differential operators n over O O . Suppose that is a prime ideal of O O of height n y 1; i.e., A s O O r is a n n n curve. We prove that every