Nilpotent elements and McCoy rings
Nilpotent elements and McCoy rings
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DOI：
10.1556/sscmath.49.2012.3.1205
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发表时间：
2012-12
影响因子：
0.7
通讯作者：
Liang Zhao;Xiaosheng Zhu;Qinqin Gu
中科院分区：
文献类型：
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作者：
Liang Zhao;Xiaosheng Zhu;Qinqin Gu
为了研究McCoy环中幂零元集的结构，引入了nil-McCoy环的概念。这个概念扩展了McCoy环和nil-Armendariz环的概念。证明了每一个半交换环都是nil-McCoy。我们将给出一个例子来证明neil - mccoy环不一定是半交换的。此外，我们还证明了nil-McCoy环不一定是正确的线性McCoy环。通过各种扩展给出了更多的nil-McCoy环的例子。另一方面，通过考虑偏多项式环R[x]中的多项式，讨论了α-McCoy环的性质；用α]代替环R[x]也进行了研究。对于环R的单态α，证明了如果R是弱α-刚性α-可逆的，则R是α- mccoy。
We introduce the concept of nil-McCoy rings to study the structure of the set of nilpotent elements in McCoy rings. This notion extends the concepts of McCoy rings and nil-Armendariz rings. It is proved that every semicommutative ring is nil-McCoy. We shall give an example to show that nil-McCoy rings need not be semicommutative. Moreover, we show that nil-McCoy rings need not be right linearly McCoy. More examples of nil-McCoy rings are given by various extensions. On the other hand, the properties of α-McCoy rings by considering the polynomials in the skew polynomial ring R[x; α] in place of the ring R[x] are also investigated. For a monomorphism α of a ring R, it is shown that if R is weak α-rigid and α-reversible then R is α-McCoy.