Idempotent and nilpotent elements in octonion rings over \(\mathbb{Z}_p\)
DOI:
https://doi.org/10.24193/subbmath.2024.1.01Abstract
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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