| 广义线性McCoy环 |
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| 引用本文： | 崔建,宋贤梅. 广义线性McCoy环[J]. 数学研究, 2013, 0(1): 47-55 |
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| 作者姓名： | 崔建 宋贤梅 |
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| 作者单位： | 安徽师范大学数学系 |
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| 基金项目： | supported by NSFC(10971024,11201064);the NSF of Jiangsu Province(BK2010393);the NSF of Anhui Educational Committee(KJ2010A126);the Research Culture Funds of Anhui Normal University(2012rcpy040) |
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| 摘 要： | 称环R是右线性McCoy的，如果R[x]中非零线性多项式f（x），g（x）满足I（x）g（x）=0，则存在非零元素r∈R使得f（x）r=0．设a是环R的自同态，通过用斜多项式环R[x；a]中的元素代替一般多项式环R[x]中的元素而引入a-线性McCoy环的概念．讨论了a-线性McCoy环的基本性质和扩张性质．
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| 关 键 词： | α-线性McCoy环 线性McCoy环 斜多项式环 |
Generalized Linearly McCoy Rings |
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| Cui Jian Song Xianmei. Generalized Linearly McCoy Rings[J]. Journal of Mathematical Study, 2013, 0(1): 47-55 |
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| Authors: | Cui Jian Song Xianmei |
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| Affiliation: | Cui Jian Song Xianmei (Department of Mathematics,Anhui Normal University,Wuhu Anhui 241003) |
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| Abstract: | A ring R is called right linearly McCoy, if whenever linear polynomials f（x）, g（x） E R[x]／{0} satisfy f（x）g（x） = 0, there exists r E R／{0} such that f（x）r = 0. For a ring endomorphism a, we introduce the notion of an a-linearly McCoy ring by considering the polynomials in the skew polynomial ring R[x; a] in place of the ring R[x]. A number of properties of this generalization are established and extension properties of a-linearly McCoy rings are given. |
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| Keywords: | a-linearly McCoy ring Linearly McCoy ring Skew polynomial ring |
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