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Strongly Gorenstein projective, injective and flat modules. (English) Zbl 1173.16006
The modules mentioned in the title are special classes of Gorenstein projective, injective, and flat modules, namely, the modules with periodic complete resolutions of period one. It is immediate, by taking the direct sum of any complete resolution with all of its shifts, that any Gorenstein projective (resp., injective, flat) is a direct summand of a strongly Gorenstein projective (resp., strongly Gorenstein injective, strongly Gorenstein flat).
The paper under review studies behavior of strongly Gorenstein modules under several operations, including various types of change of ring. Those include localizations, completions, several types of extensions, and Morita equivalence.

MSC:
16E05 Syzygies, resolutions, complexes in associative algebras
16D80 Other classes of modules and ideals in associative algebras
16E30 Homological functors on modules (Tor, Ext, etc.) in associative algebras
16E65 Homological conditions on associative rings (generalizations of regular, Gorenstein, Cohen-Macaulay rings, etc.)
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