In this paper, we give an answer to an open p roblem which was proposed in . We show that the supersemiprime radical is e qual to the near nil radical which was defined by XIE Bang_jie in .
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
We are interested in studying when the class of local modules is Baer- Kaplansky. We provide an example showing that even over a commutative semisimple ring R, we can find two non-isomorphic simple R-modules S1 and S2...We are interested in studying when the class of local modules is Baer- Kaplansky. We provide an example showing that even over a commutative semisimple ring R, we can find two non-isomorphic simple R-modules S1 and S2 such that the rings EndR(S1) and EndR(S2) are isomorphic. We show that over any ring R, the class of semisimple R-modules is Baer Kaplansky if and only if so is the class of simple R-modules.展开更多
文摘In this paper, we give an answer to an open p roblem which was proposed in . We show that the supersemiprime radical is e qual to the near nil radical which was defined by XIE Bang_jie in .
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.
文摘We are interested in studying when the class of local modules is Baer- Kaplansky. We provide an example showing that even over a commutative semisimple ring R, we can find two non-isomorphic simple R-modules S1 and S2 such that the rings EndR(S1) and EndR(S2) are isomorphic. We show that over any ring R, the class of semisimple R-modules is Baer Kaplansky if and only if so is the class of simple R-modules.