Idempotent and nilpotent elements in octonion rings over Z

Michael Aristidou, Philip R. Brown, George Chailos
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Abstract

In this paper, we show that the set O/Zp, where p is a prime number, does not form a skew field and discuss idempotent and nilpotent elements in the (finite) ring O/Zp. We provide examples and establish conditions for idempotency and nilpotency. Mathematics Subject Classification (2010): 15A33, 15A30, 20H25, 15A03. Received 27 July 2021; Accepted 14 December 2021
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Z 上八分子环中的幂等元素和零点元素
在本文中,我们证明了集合 O/Zp(其中 p 是素数)不构成一个倾斜域,并讨论了(有限)环 O/Zp 中的幂等元和零幂等元。我们举例说明并建立了幂等性和无幂性的条件:15A33, 15A30, 20H25, 15A03.2021 年 7 月 27 日收到;2021 年 12 月 14 日接受
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