Quaternion rings and octonion rings  

作　　者：Gangyong LEE Kiyoichi OSHIRO 

机构地区：[1]Department of Mathematics, Sungkyunkwan University, Suwon, Korea [2]Department of Mathematics, Yamaguchi University, Yamaguchi, Japan

出　　处：《Frontiers of Mathematics in China》2017年第1期143-155,共13页中国高等学校学术文摘·数学（英文）

摘　　要：In this paper, for rings R, we introduce complex rings C（R）, quaternion rings H（R）, and octonion rings O（R）, which are extension rings of R; R C（R） H（R） O（R）. Our main purpose of this paper is to show that if R is a Frobenius algebra, then these extension rings are Frobenius Mgebras and if R is a quasi-Frobenius ring, then C（R） and H（R） are quasi-Frobenius rings and, when Char（R）=2, O（R） is also a quasi-Frobenius ring.In this paper, for rings R, we introduce complex rings C（R）, quaternion rings H（R）, and octonion rings O（R）, which are extension rings of R; R C（R） H（R） O（R）. Our main purpose of this paper is to show that if R is a Frobenius algebra, then these extension rings are Frobenius Mgebras and if R is a quasi-Frobenius ring, then C（R） and H（R） are quasi-Frobenius rings and, when Char（R）=2, O（R） is also a quasi-Frobenius ring.

关 键 词：Hamilton quaternion numbers Cayley-Grave＇s tables complex rings quaternion rings octonion rings Frobenius algebras QF-rings 

分 类 号：O153.3[理学—数学] TQ351.472[理学—基础数学]