Recent development of Faith conjecture

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• 作者：Kazutoshi Koike ; Kiyoichi Oshiro
• 刊名：Frontiers of Mathematics in China
• 出版年：2016
• 出版时间：August 2016
• 年：2016
• 卷：11
• 期：4
• 页码：933-947
• 全文大小：169 KB
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Mathematics
  Chinese Library of Science
  
• 出版者：Higher Education Press, co-published with Springer-Verlag GmbH
• ISSN：1673-3576
• 卷排序：11

文摘

Is a semiprimary right self-injective ring a quasi-Frobenius ring? Almost half century has passed since Faith raised this problem. He first conjectured “No” in his book Algebra II. Ring Theory in 1976, but changing his mind, he conjectured “Yes” in his article “When self-injective rings are QF: a report on a problem” in 1990. In this paper, we describe recent studies of this problem based on authors works and raise related problems.KeywordsSemiprimary right self-injective ringFaith conjecturedivision algebra D(D,D)-spaceErdös-Kaplansky’s theoremquasi-Frobenius ringNakayama permutation