For a hereditary torsion theory τ, this paper mainly discuss properties of A-τ-injective modules, where A is a fixed left R-module. It is proved that if M is an A-τ-injective, B is a submodule of A, then 1） M is A...For a hereditary torsion theory τ, this paper mainly discuss properties of A-τ-injective modules, where A is a fixed left R-module. It is proved that if M is an A-τ-injective, B is a submodule of A, then 1） M is A/B-τ-injective; 2） M is B-τ-injective when B is τ-dense in A. Furthermore, we show that if A1,A2,... An, are relatively injective modules, then A1 A2 ... An is self-τ-injective if and only if A1 is self-τ-injective for each i.展开更多
In this paper, after discussing some properties of quotient contexts of a Morira context, well show that if DR is a perfect Gopriel topology, the quotient context of (P, Q), where (P, Q) as all MC between rings R and...In this paper, after discussing some properties of quotient contexts of a Morira context, well show that if DR is a perfect Gopriel topology, the quotient context of (P, Q), where (P, Q) as all MC between rings R and S is the quotient context of (P, Q), is isomorphic to a quotient context of (P, Q).展开更多
基金Supported by the National Natural Science Foundation of China(10571026)Supported by the Research Foundation of the Education Committee of Anhui Province(2006kj050c)Supported by the Doctoral Foundation of Anhui Normal University
文摘For a hereditary torsion theory τ, this paper mainly discuss properties of A-τ-injective modules, where A is a fixed left R-module. It is proved that if M is an A-τ-injective, B is a submodule of A, then 1） M is A/B-τ-injective; 2） M is B-τ-injective when B is τ-dense in A. Furthermore, we show that if A1,A2,... An, are relatively injective modules, then A1 A2 ... An is self-τ-injective if and only if A1 is self-τ-injective for each i.
文摘In this paper, after discussing some properties of quotient contexts of a Morira context, well show that if DR is a perfect Gopriel topology, the quotient context of (P, Q), where (P, Q) as all MC between rings R and S is the quotient context of (P, Q), is isomorphic to a quotient context of (P, Q).
