Quaternion rings and octonion rings

Autor: Kiyoichi Oshiro, Gangyong Lee
Rok vydání: 2016
Předmět:
Zdroj: Frontiers of Mathematics in China. 12:143-155
ISSN: 1673-3576
1673-3452
DOI: 10.1007/s11464-016-0571-6
Popis: 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 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.
Databáze: OpenAIRE
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