Abstract
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.
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References
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Lee, G., Oshiro, K. Quaternion rings and octonion rings. Front. Math. China 12, 143–155 (2017). https://doi.org/10.1007/s11464-016-0571-6
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DOI: https://doi.org/10.1007/s11464-016-0571-6
Keywords
- Hamilton quaternion numbers
- Cayley-Grave’s tables
- complex rings
- quaternion rings
- octonion rings
- Frobenius algebras
- QF-rings