Faith conjecture and related studies

2013 Fiscal Year Final Research Report

• Project/Area Number: 23540051
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Algebra
• Research Institution: Yamaguchi University
• Principal Investigator: OSHIRO kiyoichi 山口大学, その他部局等, 名誉教授 (90034727)
• Co-Investigator(Kenkyū-buntansha): BABA Yositomo 大阪教育大学, 教育学部, 教授 (10201724) ; KOIKE Kazutoshi 沖縄工業高等専門学校, 総合科学科, 教授 (20225337)
• Co-Investigator(Renkei-kenkyūsha): KIKUMASA Isao 山口大学, 理工学研究科, 教授 (70234200)
• Project Period (FY): 2011 – 2013
• Keywords: 環論 / Faith 予想 / ４元数環 / 準フロベニウ環

Research Abstract

In 1965, Osofsky showed "right injective perfect rings are QF-rings" and raised : Are right injective right perfect rings QF ?. In 1976, Faith conjectured this is not true even for semiprimary rings. Since then, almost half centuly passed. In 2011, Oshiro showed this problem is true for many cases.

Research Products

• [Journal Article] (2013)
  • Author(s): 小池寿俊
  • Journal Title: Proceedings of the 45th symposium on Ring Theory and Representation Theory Pages: 178
• [Journal Article] A construction of local QF-rings and its characterization (2012)
  • Author(s): 菊政 勲, 吉村 浩, 大城紀代市
  • Journal Title: Communication in Algebra Volume: 40 Pages: 4639-4660
  • Peer Reviewed
• [Journal Article] On the conjecture of Faith, Proceedings 6th China-Korea-Japan International Symposium on Ring Theory (2012)
  • Author(s): 大城紀代市
  • Journal Title: World Sci. Publ Pages: 152-162
  • Peer Reviewed
• [Journal Article] Classical Artinian Rings and related Topics (2012)
  • Author(s): 小池寿俊(書評) Y. Baba and K. Oshiro
  • Journal Title: 数学(日本数学会) Volume: 第64巻 Pages: 432-436
  • Peer Reviewed
• [Journal Article] Morita duality and ring extensions (2012)
  • Author(s): 小池寿俊
  • Journal Title: J. Algebra and its Appl Volume: 12, No 2 Pages: 1250160-23
  • Peer Reviewed
• [Journal Article] On almost simple injectives (2012)
  • Author(s): 馬場良始
  • Journal Title: Mathematical Journal of Okayama University Volume: 53 Pages: 101-109
  • Peer Reviewed
• [Presentation] 古典的アルチィン環と関連する話題 (2013)
  • Author(s): 馬場良始
  • Organizer: 第57回代数学シンポジウム
  • Place of Presentation: 広島大学理学部(東広島市)
  • Year and Date: 2013-08-26
• [Presentation] On the conjecture of Faith (2012)
  • Author(s): 大城紀代市
  • Organizer: OSU RING Theory Seminar talk, Ohio
  • Place of Presentation: 州立大学(米国, コロンバス市)
  • Year and Date: 2012-09-14
• [Presentation] On the conjecture of Faith (2011)
  • Author(s): 大城紀代市
  • Organizer: 6th, China-Korea-Japan International Symposium on Ring Theory
  • Place of Presentation: Kyung Hee 大学 (韓国, ソウル市)
  • Year and Date: 2011-06-28