Recent development of Faith conjecture

doi:10.1007/s11464-016-0549-4

Front. Math. China

2016, Vol. 11

Issue (4) : 933-947 https://doi.org/10.1007/s11464-016-0549-4

RESEARCH ARTICLE

Recent development of Faith conjecture

Kazutoshi KOIKE^1,^*(

),Kiyoichi OSHIRO²

¹. Okinawa National College of Technology, Okinawa, Japan
². Yamaguchi University, Yamaguchi, Japan

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Abstract

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.

Keywords Semiprimary right self-injective ring Faith conjecture division algebra D (D D)-space Erdös-Kaplansky’s theorem quasi-Frobenius ring Nakayama permutation

Corresponding Author(s): Kazutoshi KOIKE

Issue Date: 30 August 2016

Cite this article:

Kazutoshi KOIKE,Kiyoichi OSHIRO. Recent development of Faith conjecture[J]. Front. Math. China, 2016, 11(4): 933-947.

URL:

https://academic.hep.com.cn/fmc/EN/10.1007/s11464-016-0549-4
https://academic.hep.com.cn/fmc/EN/Y2016/V11/I4/933

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