Generators of $\displaystyle \mathbb{Z}$ are $\displaystyle <1> \ \text{and} \ <-1>$ correct?

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- Oct 3rd 2011, 02:22 PMdwsmithSimple question
Generators of $\displaystyle \mathbb{Z}$ are $\displaystyle <1> \ \text{and} \ <-1>$ correct?

- Oct 3rd 2011, 02:38 PMalexmahoneRe: Simple question
- Oct 3rd 2011, 02:45 PMdwsmithRe: Simple question
- Oct 3rd 2011, 02:47 PMalexmahoneRe: Simple question
- Oct 3rd 2011, 02:51 PMdwsmithRe: Simple question
- Oct 3rd 2011, 02:57 PMalexmahoneRe: Simple question
$\displaystyle <n>$ denotes the subgroup generated by $\displaystyle n$.

So, $\displaystyle <1>=<-1>=\mathbb{Z}$

It doesn't make sense to say that the generators of $\displaystyle \mathbb{Z}$ are $\displaystyle \mathbb{Z}$ and $\displaystyle \mathbb{Z}$, which is what you essentially did. - Oct 3rd 2011, 03:00 PMdwsmithRe: Simple question
- Oct 3rd 2011, 03:07 PMalexmahoneRe: Simple question
- Oct 3rd 2011, 03:27 PMalexmahoneRe: Simple question
See Example 1.4 of http://www.math.uconn.edu/~kconrad/b...ory/genset.pdf.

- Oct 3rd 2011, 03:33 PMdwsmithRe: Simple question
- Oct 3rd 2011, 03:40 PMalexmahoneRe: Simple question