692,526 research outputs found
Relative FP-injective and FP-flat complexes and their model structures
In this paper, we introduce the notions of -injective and -flat complexes in terms of complexes of type . We show that
some characterizations analogous to that of injective, FP-injective and flat
complexes exist for -injective and -flat complexes. We
also introduce and study -injective and -flat
dimensions of modules and complexes, and give a relation between them in terms
of Pontrjagin duality. The existence of pre-envelopes and covers in this
setting is discussed, and we prove that any complex has an -flat
cover and an -flat pre-envelope, and in the case that
any complex has an -injective cover and an -injective
pre-envelope. Finally, we construct model structures on the category of
complexes from the classes of modules with bounded -injective and
-flat dimensions, and analyze several conditions under which it is
possible to connect these model structures via Quillen functors and Quillen
equivalences.Comment: 41 page
FP-GR-INJECTIVE MODULES
In this paper, we give some characterizations of FP-grinjective R-modules and graded right R-modules of FP-gr-injective dimension at most n. We study the existence of FP-gr-injective envelopes and FP-gr-injective covers. We also prove that (1) (⊥gr-FI, gr-FI) is a hereditary cotorsion theory if and only if R is a left gr-coherent ring, (2) If R is right gr-coherent with FP-gr-id(RR) ≤ n, then (gr-FIn, gr-F n⊥) is a perfect cotorsion theory, (3) (⊥gr-FIn, gr-FIn) is a cotorsion theory, where gr-FI denotes the class of all FP-gr-injective left R-modules, gr-FIn is the class of all graded right R-modules of FP-gr-injective dimension at most n. Some applications are given
- …