SEMINAR: THE OSU-OU RING THEORY SEMINAR

 TITLE:  On the Faith conjecture and local QF-rings with radical cubed zero

 SPEAKER:      Kiyoichi Oshiro

                        Yamaguchi University, Japan

 DAY/DATE: FRIDAY, August 18, 2006

 TIME:          4:45 P.M.

 ROOM:        MW 154

ABSTRACT: In 1976, in his Book "Algebra II", Faith conjectured "no" for the problem: Are semiprimary right

self-injective rings quasi-Frobenius.? Since that time, this conjecture is known by the Faith conjecture. Although

many ring theorists have tried to solve this conjecture, the conjecture still remains open. In my talk, first, I

translate this problem into a problem on two-sided vector spaces. In some sense, the difficulty of this problem

stems from the question: Can we make freely non-commutative local QF-rings ? In connection with my translation of

the Faith conjecture, I present my construction of local QF-rings with radical cubed zero using a field of complex

numbers, quaternion of Hamilton or number fields etc.