Complexes of gorenstein flat modules and gorenstein cotorsion modules

摘要

A complex (C, δ) is called strongly Gorenstein flat if C is exact and Ker δ~n is Gorenstein flat in R-Mod for all n ε ?. Let JG stand for the class of strongly Gorenstein flat complexes. We show that a complex C of left R-modules over a right coherent ring R is in the right orthogonal class of JG if and only if C~n is Gorenstein cotorsion in R-Mod for all n ε ? and Hom(G, C) is exact for any strongly Gorenstein flat complex G. Furthermore, a bounded below complex C over a right coherent ring R is in the right orthogonal class of JG if and only if C~n is Gorenstein cotorsion in R-Mod for all n ε ?. Finally, strongly Gorenstein flat covers and JG~({box drawings light up and horizontal}) -envelopes of complexes are considered. For a right coherent ring R, we show that every bounded below complex has a JG~({box drawings light up and horizontal}) -envelope.