共查询到10条相似文献,搜索用时 234 毫秒
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环$R$称为是半clean的, 是指环中的每个元素都是一个单位与一个周期元的和. clean环是半clean的. 刻画半clean群环的一般情形是不容易的. 我们的目的是考虑如下问题:若$G$ 是局部有限群或者是阶是3的循环群, 群环$RG$何时是semiclean的. clean群环上的一些已有结果被推广. 相似文献
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Evrim Akalan 《代数通讯》2017,45(2):694-697
Let R be a commutative Noetherian domain and A be a polycyclic-by-finite group. In this paper, it is determined, in terms of properties of R and A when the group ring R[A] is a G-Dedekind prime ring. 相似文献
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Let R be an associative ring with identity.R is said to be semilocal if R/J(R)is(semisimple)Artinian,where J(R)denotes the Jacobson radical of R.In this paper,we give necessary and sufficient conditions for the group ring RG to be semilocal,where G is a locally finite nilpotent group. 相似文献
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将Minkowski关于有限整数矩阵群的著名结果推广到一般的环上,主要结果是证明了:对任意环R,如果R的加法群为有限生成的自由Abel群,则R的所有乘法可逆元构成的群U(R)中的有限子群精确到同构只有有限多个. 相似文献
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For a torsion or torsion-free group G and a field F, we characterize the group algebra FG that is Armendariz. Armendariz property for a group ring over a general ring R is also studied and related to those of Abelian group rings and the quaternion ring over R. 相似文献
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Let R *θG be the skew group ring with a F.C group G and the group homom-rphismθfrom G to Aut(R), the group of automorphisms of the ring R. In this paper,the necessary and sufficient condition such that R*θG will be Noetherian is given, which generalizes the results of I.G. connel. 相似文献
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WANG XIU-LAN 《东北数学》2012,28(1)
A ring R is called clean if every element is the sum of an idempotent and a unit,and R is called uniquely strongly clean (USC for short) if every element is uniquely the sum of an idempotent and a unit... 相似文献
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Angelina Y. M. Chin 《Czechoslovak Mathematical Journal》2002,52(4):749-755
Let R be an associative ring with identity and let J(R) denote the Jacobson radical of R. R is said to be semilocal if R/J(R) is Artinian. In this paper we give necessary and sufficient conditions for the group ring RG, where G is an abelian group, to be semilocal. 相似文献
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