Algebra Solutions: Find a presentation for ZZ/(n)

Find a presentation for ZZ/(n)

Find a set of generators and relations for $\mathbb{Z}/(n)$ .

We saw in a previous exercise that the distinct elements of $\mathbb{Z}/(n)$ are precisely $\overline{0}, \overline{1}, \ldots \overline{n-1}$ . Note that these are precisely the multiples of $\overline{1}$ ; hence $\mathbb{Z}/(n)$ is generated by $\overline{1}$ . Since $|\overline{1}| = n$ , we have $\mathbb{Z}/(n) = \langle x \ |\ x^n = 1 \rangle$ .

Algebra Solutions

Find a presentation for ZZ/(n)

No comments:

Post a Comment