Idempotent and nilpotent elements in octonion rings over \(\mathbb{Z}_p\)

Michael Aristidou, Philip R. Brown, George Chailos

Abstract


 

In this paper, we show that the set \(\mathbb{O}/\mathbb{Z}_p\), where \(p\) is a prime number, does not form a skew field and discuss idempotent and nilpotent elements in the (finite) ring \(\mathbb{O}/\mathbb{Z}_p\). We provide examples and establish conditions for idempotency and nilpotency.


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DOI: http://dx.doi.org/10.24193/subbmath.2024.1.01

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