In this paper, we definde the dual semimodule and reflexive semimodule in the category of semimodules and completely generalize the results of dual modules and reflexive modules to the dual semimodules and reflexive s...In this paper, we definde the dual semimodule and reflexive semimodule in the category of semimodules and completely generalize the results of dual modules and reflexive modules to the dual semimodules and reflexive semimodules.展开更多
In the paper, we define（inco） project modules of relatively hereditary torsion theory τ by intersection complement of module and study their properties; secondly, we define the（inco） τ-semisimple ring by（inco）...In the paper, we define（inco） project modules of relatively hereditary torsion theory τ by intersection complement of module and study their properties; secondly, we define the（inco） τ-semisimple ring by（inco） τ-projective module and study their properties. When r is a trivial torsion theory on R-rood, we prove that R is a semisimple ring if and only if R is a（inco） semisimple ring and satisfies（inco） condition.展开更多
文摘In this paper, we definde the dual semimodule and reflexive semimodule in the category of semimodules and completely generalize the results of dual modules and reflexive modules to the dual semimodules and reflexive semimodules.
基金Supported by the Science and Technology Develop Foundation of Jilin Science and Technology Department(20040506-3)
文摘In the paper, we define（inco） project modules of relatively hereditary torsion theory τ by intersection complement of module and study their properties; secondly, we define the（inco） τ-semisimple ring by（inco） τ-projective module and study their properties. When r is a trivial torsion theory on R-rood, we prove that R is a semisimple ring if and only if R is a（inco） semisimple ring and satisfies（inco） condition.
