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May 27, 2020 at 0:30 comment added Arturo Magidin @Group23: And as I indicated, they are just the ideal generated by the corresponding element. $\langle 7\rangle/\langle 63\rangle$ in $\mathbb{Z}/\langle 63\rangle$ is the same as $\langle 7\rangle$ in $\mathbb{Z}_{63}$.
May 26, 2020 at 23:50 comment added Partey5 What I meant is I don’t know to write these in non-quotient form.
May 26, 2020 at 23:45 comment added J. W. Tanner “to contain is to divide”
May 26, 2020 at 23:43 comment added Arturo Magidin @Group23: They are the same thing. $\langle 7\rangle/\langle 63\rangle$ is the ideal generated by $7$ in $\mathbb{Z}_{63}$.
May 26, 2020 at 23:25 comment added Partey5 That helps. I now know that there are 6 ideals of $\mathbb{Z}_{63}$. However I only know what these are in the quotient form e.g. $\langle 7 \rangle / \langle 63 \rangle$
May 26, 2020 at 23:00 history answered Arturo Magidin CC BY-SA 4.0