MAT3004 Abstract Algebra I

Deliberately flawed arguments about groups, rings, and fields. Each topic begins with one example, presented as a FakeGPT conversation.

  1. Identify exactly where the proof goes wrong.
  2. Decide whether the original statement is correct. Give a correct proof or a counterexample.
Groups1 exampleMust a group of order pqpq be cyclic when p,qp,q are distinct primes? Rings1 exampleDoes a prime ideal remain prime when extended to a polynomial ring? Fields1 exampleDoes every element outside the base field generate an extension of prime degree?