Article ID Journal Published Year Pages File Type
5771860 Journal of Algebra 2017 12 Pages PDF
Abstract
Let R be an associative ring with unit and denote by FM the class of all flat and Mittag-Leffler left R-modules. In [4] it is proved that, if R is countable, the orthogonal class of FM consists of all cotorsion modules. In this note we extend this result to the class of all rings R satisfying that each flat left R-module is filtered by totally ordered direct limits of projective modules. This class of rings contains all countable, left perfect and discrete valuation domains. Moreover, assuming that there do not exist inaccessible cardinals, we obtain that, over these rings, all flat left R-modules have finite projective dimension.
Related Topics
Physical Sciences and Engineering Mathematics Algebra and Number Theory
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