FP-GR-INJECTIVE MODULES
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概要
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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) (<sup>⊥</sup>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(R<sub>R</sub>) ≤ n, then (gr-FI<sub>n</sub>, gr-F <sub>n</sub><sup>⊥</sup>) is a perfect cotorsion theory, (3) (<sup>⊥</sup>gr-FI<sub>n</sub>, gr-FI<sub>n</sub>) is a cotorsion theory, where gr-FI denotes the class of all FP-gr-injective left R-modules, gr-FI<sub>n</sub> is the class of all graded right R-modules of FP-gr-injective dimension at most n. Some applications are given.
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