Recent development of Faith conjecture  

作　　者：Kazutoshi KOIKE Kiyoichi OSHIRO 

机构地区：[1]Okinawa National College of Technology, Okinawa, Japan [2]Yamaguchi University, Yamaguchi, Japan

出　　处：《Frontiers of Mathematics in China》2016年第4期933-947,共15页中国高等学校学术文摘·数学（英文）

摘　　要：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.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.

关 键 词：Semiprimary right self-injective ring Faith conjecture division algebra D （D D）-space ErdSs-Kaplansky＇s theorem quasi-Frobenius ring Nakayama permutation 

分 类 号：O153.3[理学—数学]