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| 摘要: |
| 本文研究诣零半交换环上的Ore扩张环的性质.利用对多项式的逐项分析方法,我们证明了:设α是环R上的一个自同态,δ是环R上的一个α-导子.如果R是(α,δ)-斜Armendariz的(α,δ)-compatible环,则R[x;α,δ]是诣零半交换环当且仅当环R是诣零半交换环;如果R是诣零半交换的(α,δ)-compatible环,则R[x;α,δ]是斜Armendariz环.所得结果推广了近期关于斜多项式环的相关结论. |
| 关键词: 诣零半交换环 Ore扩张 (α,δ)-compatible环 弱(α,δ)-compatible环 (α,δ)-斜Armendari环 弱(α,δ)-斜Armendari环 |
| DOI： |
| 分类号:O153.3 |
| 基金项目:Supported by the National Natural Science Foundation of China (11101217) and the Natural Science Foundation of Jiangsu Province (BK20141476). |
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| ORE EXTENSIONS OF NIL-SEMICOMMUTATIVE RINGS |
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WANG Yao,JIANG Mei-mei,REN Yan-li
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| Abstract: |
| In this paper, we study the properties of Ore extensions of nil-semicommutative rings. Let α be an endomorphism and δ an α-derivation of a ring R. By using the itemized analysis method on polynomials, we prove that if R is (α, δ)-skew Armendariz and (α, δ)-compatible, then R[x;α,δ] is nil-semicommutative if and only if R is nil-semicommutative; if R is nil-semicommutative and (α, δ)-compatible, then R[x;α,δ] is weak Armendariz, which generalize some related work on skew polynomial rings. |
| Key words: nil-semicommutative ring Ore extension (α,δ)-compatible ring weak(α,δ)-compatible ring (α,δ)-skew Armendariz ring weak(α,δ)-skew Armendariz ring |
