Let n≥1 be an integer.In this article,we study the notions of Cartan-Eilenberg FP_(n)injective and Cartan-Eilenberg FP_(n)-flat complexes.We also investigate duality pairs relative to the Cartan-Eilenberg FP_(n)-inje...Let n≥1 be an integer.In this article,we study the notions of Cartan-Eilenberg FP_(n)injective and Cartan-Eilenberg FP_(n)-flat complexes.We also investigate duality pairs relative to the Cartan-Eilenberg FP_(n)-injective and Cartan-Eilenberg FP_(n)-flat complexes.As applications,we obtain that any complex admits Cartan-Eilenberg FP_(n)-injective(resp.,Cartan-Eilenberg FP_(n)-flat)cover and preenvelope and we characterize left n-coherent rings using these two classes of complexes.展开更多
In this paper,we study the relations between the class of A-Gorenstein projective modules and the left orthogonal class of A,also the relations between the class of A-Gorenstein injective modules and the right orthogo...In this paper,we study the relations between the class of A-Gorenstein projective modules and the left orthogonal class of A,also the relations between the class of A-Gorenstein injective modules and the right orthogonal class of A.Some functor characterizations of AGorenstein projective modules and A-Gorenstein injective modules are obtained.Using the notion of complete duality pair,we discuss the relations between A-Gorenstein projective modules and B-Gorenstein flat modules.Some known results are generalized.展开更多
By the theory of Modern Geometry, the mechanical principle and advanced calculus, the dynamics in Newtonian_Galilean spacetime is generalized to Newtonian_Riemannian Spacetime, and the dynamics in N_R spacetime is est...By the theory of Modern Geometry, the mechanical principle and advanced calculus, the dynamics in Newtonian_Galilean spacetime is generalized to Newtonian_Riemannian Spacetime, and the dynamics in N_R spacetime is established. Being divided it into some parts. This paper is one of them. The others are to be continued.展开更多
基金Supported by the National Natural Science Foundation of China(Grant No.12061061)the Science and Technology Project of Gansu Province(Grant No.22JR5RA153).
文摘Let n≥1 be an integer.In this article,we study the notions of Cartan-Eilenberg FP_(n)injective and Cartan-Eilenberg FP_(n)-flat complexes.We also investigate duality pairs relative to the Cartan-Eilenberg FP_(n)-injective and Cartan-Eilenberg FP_(n)-flat complexes.As applications,we obtain that any complex admits Cartan-Eilenberg FP_(n)-injective(resp.,Cartan-Eilenberg FP_(n)-flat)cover and preenvelope and we characterize left n-coherent rings using these two classes of complexes.
基金Supported by Qinglan Project of Jiangsu Province(Grant No.2022)the National Natural Science Foundation of China(Grant No.11701408)Jiangsu Provincial Government Scholarship Program。
文摘In this paper,we study the relations between the class of A-Gorenstein projective modules and the left orthogonal class of A,also the relations between the class of A-Gorenstein injective modules and the right orthogonal class of A.Some functor characterizations of AGorenstein projective modules and A-Gorenstein injective modules are obtained.Using the notion of complete duality pair,we discuss the relations between A-Gorenstein projective modules and B-Gorenstein flat modules.Some known results are generalized.
文摘By the theory of Modern Geometry, the mechanical principle and advanced calculus, the dynamics in Newtonian_Galilean spacetime is generalized to Newtonian_Riemannian Spacetime, and the dynamics in N_R spacetime is established. Being divided it into some parts. This paper is one of them. The others are to be continued.
