FPn-injective and FPn-flat modules with respect to a semidualizing bimodule
W Wu, Z Gao - Communications in Algebra, 2022 - Taylor & Francis
W Wu, Z Gao
Communications in Algebra, 2022•Taylor & FrancisLet S and R be rings, SCR be a semidualizing bimodule and n≥ 0 be an integer or n=∞.
We introduce and study C-FP n-injective and C-FP n-flat modules as a common
generalization of some known modules such as C-injective (resp. C-FP-injective, C-weak
injective) and C-flat (resp. C-projective, C-weak flat) modules. Suppose that SCR is a
faithfully semidualizing bimodule. We give some equivalent characterizations of left n-
coherent rings in terms of C-FP n-flat left S-modules and C-FP n-injective left R-modules …
We introduce and study C-FP n-injective and C-FP n-flat modules as a common
generalization of some known modules such as C-injective (resp. C-FP-injective, C-weak
injective) and C-flat (resp. C-projective, C-weak flat) modules. Suppose that SCR is a
faithfully semidualizing bimodule. We give some equivalent characterizations of left n-
coherent rings in terms of C-FP n-flat left S-modules and C-FP n-injective left R-modules …
Abstract
Let S and R be rings, be a semidualizing bimodule and be an integer or We introduce and study C-FPn-injective and C-FPn-flat modules as a common generalization of some known modules such as C-injective (resp. C-FP-injective, C-weak injective) and C-flat (resp. C-projective, C-weak flat) modules. Suppose that is a faithfully semidualizing bimodule. We give some equivalent characterizations of left n-coherent rings in terms of C-FPn-flat left S-modules and C-FPn-injective left R-modules. Then we show that the pairs and are coproduct-closed and product-closed duality pairs and both and are covering and preenveloping, where and denote the classes of C-FPn-flat left S-modules and C-FPn-injective left R-modules respectively. Finally, we investigate Foxby equivalence relative to C-FPn-injective and C-FPn-flat modules.
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