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On *-clean group rings over abelian groups
Han, Dongchun1; Ren, Yuan2; Zhang, Hanbin3
2017-08-01
Source PublicationJOURNAL OF ALGEBRA AND ITS APPLICATIONS
ISSN0219-4988
Volume16Issue:8Pages:11
AbstractAn associative ring with unity is called clean if each of its elements is the sum of an idempotent and a unit. A clean ring with involution * is called *-clean if each of its elements is the sum of a unit and a projection (*-invariant idempotent). In a recent paper, Huang, Li and Yuan provided a complete characterization that when a group ring F(q)C(p)k is *-clean, where F-q is a finite field and C(p)k is a cyclic group of an odd prime power order p(k). They also provided a necessary condition and a few sufficient conditions for FqCn to be *-clean, where C-n is a cyclic group of order n. In this paper, we extend the above result of Huang, Li and Yuan from F(q)C(p)k to FG and provide a characterization of *-clean group rings FG, where G is a finite abelian group and F is a field with characteristic not dividing the exponent of G.
KeywordGroup ring *-clean ring Galois group idempotent
DOI10.1142/S0219498817501523
Language英语
WOS Research AreaMathematics
WOS SubjectMathematics, Applied ; Mathematics
WOS IDWOS:000403428300012
PublisherWORLD SCIENTIFIC PUBL CO PTE LTD
Citation statistics
Cited Times:1[WOS]   [WOS Record]     [Related Records in WOS]
Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/25585
Collection中国科学院数学与系统科学研究院
Affiliation1.Southwest Jiaotong Univ, Dept Math, Chengdu 610000, Peoples R China
2.Chinese Acad Sci, Morningside Ctr Math, Acad Math & Syst Sci, Beijing 100190, Peoples R China
3.Nankai Univ, Ctr Combinator, Tianjin 300071, Peoples R China
Recommended Citation
GB/T 7714
Han, Dongchun,Ren, Yuan,Zhang, Hanbin. On *-clean group rings over abelian groups[J]. JOURNAL OF ALGEBRA AND ITS APPLICATIONS,2017,16(8):11.
APA Han, Dongchun,Ren, Yuan,&Zhang, Hanbin.(2017).On *-clean group rings over abelian groups.JOURNAL OF ALGEBRA AND ITS APPLICATIONS,16(8),11.
MLA Han, Dongchun,et al."On *-clean group rings over abelian groups".JOURNAL OF ALGEBRA AND ITS APPLICATIONS 16.8(2017):11.
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