On *-Clean Group Rings II
On *-Clean Group Rings II
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DOI：
10.1080/00927872.2015.1044106
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发表时间：
2016-06
影响因子：
0.7
通讯作者：
Hongdi Huang;Yuanlin Li;P. Yuan
中科院分区：
文献类型：
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作者：
Hongdi Huang;Yuanlin Li;P. Yuan
如果其每个元素都是单位和投影的总和（ *-invariant didempotent），则称为 * - 清洁。最近，Gao，Chen和Li获得了RG为 * - 清洁的必要条件，其中R是换向的局部环，G是C3，C4，S3和Q8之一。最近，Li，Yuan和Parmenter给出了何时代数FCP的完整表征，其中F是一个字段，而CP是Prime Order prorder p的循环组。在本文中，我们将上述结果从FCP扩展到FQCPK，其中FQ是一个有限的字段，CPK是一个奇数Prime Power Order PK的循环基团。对于G = Cn是循环n阶n的一般情况，我们还提供了必要的条件和一些足够的条件，使FQCN成为 * - 清洁。
A ring with involution * is called *-clean if each of its elements is the sum of a unit and a projection (*-invariant idempotent). Recently, Gao, Chen, and Li obtained necessary and sufficient conditions for RG to be *-clean, where R is a commutative local ring and G is one of C3, C4, S3, and Q8. Most recently, Li, Yuan, and Parmenter gave a complete characterization of when the group algebra FCp is *-clean, where F is a field and Cp is a cyclic group of prime order p. In this article, we extend the above mentioned result from FCp to FqCpk, where Fq is a finite field and Cpk is a cyclic group of an odd prime power order pk. For the general case when G = Cn is cyclic group of order n, we also provide a necessary condition and a few sufficient conditions for FqCn to be *-clean.