Skip to content
Part CCSIR NET December 2024analytic-zeros-are-isolated-and-continuous-ones-are-not

Analytic zeros are isolated and continuous ones are not

Which of the following rings are integral domains?

  1. A.The ring of polynomials in 3 variables over R\mathbb{R}.✓ Correct
  2. B.The ring of complex analytic functions on the open unit disc in C\mathbb{C}.✓ Correct
  3. C.The ring of 2 × 2 real matrices.
  4. D.The ring of continuous functions from [0, 1] to R\mathbb{R}.

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, and why this one tests standard counterexample.

See pricing

50 are analysed free — try those first.

The trap it tests

Standard counterexample

There is a canonical object that settles this. Recognising it is the whole question.

Drill statements like this

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 Fields › Ideals, quotient rings, prime & maximal ideals, CRT

Last revised . Found a mistake? Tell us — corrections are the fastest thing we act on.

ShareWhatsAppTelegram