# 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.