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Strict Mittag-Leffler conditions and Gorenstein modules. (English) Zbl 1367.16006

Summary: In this paper, firstly, we characterize some rings by strict Mittag-Leffler conditions. Then, we investigate when Gorenstein projective modules are Gorenstein flat by employing tilting modules and cotorsion pairs. Finally, we study the direct limits of Gorenstein projective modules.

MSC:

16E65 Homological conditions on associative rings (generalizations of regular, Gorenstein, Cohen-Macaulay rings, etc.)
13D02 Syzygies, resolutions, complexes and commutative rings
13E05 Commutative Noetherian rings and modules
16D10 General module theory in associative algebras
16D80 Other classes of modules and ideals in associative algebras
16D90 Module categories in associative algebras
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