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Part CCSIR NET June 2024crt-splits-the-ideal-lattice

Crt splits the ideal lattice

Let I be an ideal of the ring 𝔽. Which of the following are the possible values for the cardinality of I?

  1. A.1
  2. B.8
  3. C.16
  4. D.24

You have the answer. Trap Analysis is why the other three were written.

Not a worked solution repeated four times — the specific reasoning error each wrong option was built to reward.

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50 are analysed free — try those first.

Related counterexample: Every prime ideal is maximal

More on this topic

The chapter behind this: Ideals, quotients and the Chinese remainder theorem — free to read

From Rings and FieldsIdeals, quotient rings, prime & maximal ideals, CRT

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