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Abstract Algebra

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Moderate

Ideals of a Product Ring: Counting Them in an Example

ABSALG-EYBCX3

How many distinct ideals are there in $\mathbb{Z}/6\mathbb{Z} \times \mathbb{Z}/10\mathbb{Z}$?

A

$2$

B

$7$

C

$8$

D

$15$

E

$16$