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Quaternion rings and octonion rings |
Gangyong LEE1,Kiyoichi OSHIRO2( ) |
1. Department of Mathematics, Sungkyunkwan University, Suwon, Korea
2. Department of Mathematics, Yamaguchi University, Yamaguchi, Japan |
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Abstract In this paper, for rings R, we introduce complex rings ℂ(R), quaternion rings ℍ(R), and octonion rings О, 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 algebras 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.
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| Keywords
Hamilton quaternion numbers
Cayley-Grave’s tables
complex rings
quaternion rings
octonion rings
Frobenius algebras
QF-rings
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Corresponding Author(s):
Kiyoichi OSHIRO
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Issue Date: 17 November 2016
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| 1 |
Hoshino M, Kameyama N, Koga H. Construction of Auslander-Gorenstein Local Rings. Proceeding of the 45th Symposium on Ring Theory and Representation Theory, Shinshu University, 2012
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| 2 |
Nicholson W K. Introduction to Abstract Algebra. Boston: PWS-KENT Publishing Company, 1993
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