Find all the maximal ideals of the ring $\mathbb Z_4 \oplus \mathbb Z_{15}$.
The maximal ideal should be of the form $<1> \oplus <p>$ or $<p> \oplus <1>$ where $p$ is a prime and common divisor of $4$ and $15$? Am I correct?
2026-04-04 04:10:01.1775275801
Find all maximal ideals of the ring $\mathbb Z_4 \oplus \mathbb Z_{15}$
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You are not correct. The maximal ideals are of the form you mentioned, but $p\mid 4$ in one case, and $p\mid 15$ in the other case. So $2\mathbb Z_4\oplus\mathbb Z_{15}$, $\mathbb Z_4\oplus3\mathbb Z_{15}$, and $\mathbb Z_4\oplus5\mathbb Z_{15}$ are the maximal ideals.