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arXiv · 2606.02975

Diagonal Condition in Multiplication Table of $\displaystyle {\, \mathbb{Z} [i] / (\alpha) }$

Chadaphorn Kodsueb
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Abstract

Multiplication table of a ring with identity 1 is said to have the diagonal condition if 1s occur only on the main diagonal. In this paper, we study the diagonal condition in the ring of Gaussian integers $\mathbb{Z}[i]$. Furthermore, we also find the Gaussian integers $\alpha$ so that the rings of Gaussian integers modulo $\alpha$ satisfy the diagonal condition.

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Chadaphorn Kodsueb. 2026-06-02. Diagonal Condition in Multiplication Table of $\displaystyle {\, \mathbb{Z} [i] / (\alpha) }$. https://arxiv.org/abs/2606.02975

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