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OSA: Algebra

Question 1

Which of the following claims are correct?

claimcorrect?resultexplanation

If \(G\) is a finite group and \(N\) a normal subgroup of \(G\), then \(G\) has a subgroup \(H\) that forms a system of representatives for the cosets of \(N\).

For every field \(K\), the ring \(K[x,y]\) of polynomials in two indeterminates is a principal ideal ring.

For every field \(K\), the ring \(K[x]\) of polynomials in one indeterminate is a euclidean ring.