# OSA: Algebra

## Question 1

Which of the following claims are correct?

claim | correct? | result | explanation |
---|---|---|---|

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. |