| ON ORDER RINGS OF SEMI-PRIMARY RINGS |
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| 作者姓名： | Xu Yonghua |
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| 作者单位： | Institute of |
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| 基金项目： | Project supported by the Science Fund of the Chinese Academy of Sciences. |
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| 摘 要： | The main results of this paper are stated as follows.Let R be an orderring in thesemi-primary ring Q.Suppose that R satisfies the maximal condition for nil right ideals ofR,Then we have(i)if an ideal I of R has a finite length as right R-module,then I alsohas a finite length as left R-module;(ii)denote by A(R)the Artinian radical of R,andN the nil radical of R,then A(R)+N/N=A(R/N),if R satisfies the commutative condi-tion on the zero product of prime ideals of B.
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| 收稿时间： | 1987/9/29 0:00:00 |
| 修稿时间： | 1988/9/30 0:00:00 |
On Order Rings of Semi-Primary Rings |
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| Xu Yonghua.ON ORDER RINGS OF SEMI-PRIMARY RINGS[J].Chinese Annals of Mathematics,Series B,1990,11(4):503-512. |
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| Authors: | Xu Yonghua |
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| Institution: | Institute of Mathematics,Fudan University,Shanghai,China. |
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| Abstract: | The main results of this paper are stated as follows. Let R be an orderring in the semi-primary ring Q. Suppose that R satisfies the maximal condition for nil right ideals of R, Then we have (i) if an ideal I of R has a finite length as right R-module, then I also ihas a finite length as left R-module; (ii) denote by A(R) the Artinian radical of R, and N the nil radical of R, then A(R) +N /N=A(R/N), if R satisfies the commutative condition on the zero product of prime ideals of R. |
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