| 摘要: |
| 本文研究具有对称自同态和对称导子的环. 利用性质nil(R[x]) =nil(R)[x], 我们证明了: 如果R是弱2-primal 环, 则R 是弱对称(σ, δ)-环当且仅当R[x] 是弱对称(σ,δ) -环. 本文结论拓展了关于对称环和弱对称环的研究. |
| 关键词: 对称环 对称σ-环 弱对称(σ,δ)-环 弱2-primal 环 |
| DOI： |
| 分类号:O153.3 |
| 基金项目:Supported by National Natural Science Foundation of China(11101217); Nat-ural Science Foundation of Jiangsu Province of China (BK20141476). |
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| ON RINGS WITH SYMMETRIC ENDOMORPHISMS AND SYMMETRIC DERIVATIONS |
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WANG Yao1, WANG Wei-liang2, REN Yan-li3
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1.School of Math. and Stat., Nanjing University of Information Science and Technology, Nanjing 210044, China;2.School of Electrical Engineering and Automation, Tianjin University, Tianjin 300072, China;3.School of Mathematics and Information Technology, Nanjing Xiaozhuang University, Nanjing 211171, China
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| Abstract: |
| In this paper, we study rings with symmetric endomorphisms and symmetric derivations. By using the property nil(R[x]) =nil(R)[x], we show that if R is weakly 2-primal, then R is a weak symmetric (σ,δ)-ring if and only if R[x] is a weak symmetric (σ,δ)-ring, which extend the research on symmetric rings and weak symmetric rings. |
| Key words: symmetric ring symmetric σ-ring weak symmetric (σ,δ)-ring weak 2-primal ring |
