ON WEAK ARMENDARIZ RINGS
ON WEAK ARMENDARIZ RINGS
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DOI：
10.4134/bkms.2009.46.1.135
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发表时间：
2009-01
影响因子：
0.5
通讯作者：
Y. Jeon;H. Kim;Yang Lee;Jung Sook Yoon
中科院分区：
文献类型：
--
作者：
Y. Jeon;H. Kim;Yang Lee;Jung Sook Yoon
本文研究了弱Armendariz环的性质，以及弱Armendariz环、Armendariz环、约化环和IFP环之间的联系。证明了右Ore环R是弱Armendariz环当且仅当Q是弱Armendariz环，其中Q是R的经典右商环.借助于这个结果，我们证明了半素右Goldie环R是弱Armendariz当且仅当R是Armendariz当且仅当R是约化的当且仅当R是IFP当且仅当Q是除环的有限直积，从而得到了Lee和Wong结果的一个简单证明.在这个过程中，我们构造了一个半质环扩张是无限维的，从给定的任何半质环。接下来我们将找到更多弱Armendariz环的例子。
In the present note we study the properties of weak Armen- dariz rings, and the connections among weak Armendariz rings, Armen- dariz rings, reduced rings and IFP rings. We prove that a right Ore ring R is weak Armendariz if and only if so is Q, where Q is the classical right quotient ring of R. With the help of this result we can show that a semiprime right Goldie ring R is weak Armendariz if and only if R is Armendariz if and only if R is reduced if and only if R is IFP if and only if Q is a nite direct product of division rings, obtaining a simpler proof of Lee and Wong's result. In the process we construct a semiprime ring extension that is innite dimensional, from given any semiprime ring. We next nd more examples of weak Armendariz rings.