On the flat length of injective modules

In this paper, we use the notion of strict Mittag-Leffler modules, in order to study the flat length of injective modules over a ring R. We show that the supremum of these flat lengths is closely related to the invariants silp R and spli R, which were defined by Gedrich and Gruenberg, as well as to...

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Bibliographic Details
Published in:Journal of the London Mathematical Society 2011-10, Vol.84 (2), p.408-432
Main Authors: Emmanouil, Ioannis, Talelli, Olympia
Format: Article
Language:English
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Summary:In this paper, we use the notion of strict Mittag-Leffler modules, in order to study the flat length of injective modules over a ring R. We show that the supremum of these flat lengths is closely related to the invariants silp R and spli R, which were defined by Gedrich and Gruenberg, as well as to the finitistic dimension of R and the injective length of the regular module. We also examine the special case where R= G is the integral group ring of a group G.
ISSN:0024-6107
1469-7750
DOI:10.1112/jlms/jdr014