Let p be a fixed prime, and let R be the subring ofQconsisting of all rational numbers a/b with (b,p) = 1.

a) Show that R has a unique maximal ideal M.

b) What are the prime ideals of R?

c) Show that R/M is isomorphic toZ/pZ.

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- May 4th 2013, 11:26 AMheejenna55maximal and prime ideals question
Let p be a fixed prime, and let R be the subring of

**Q**consisting of all rational numbers a/b with (b,p) = 1.

a) Show that R has a unique maximal ideal M.

b) What are the prime ideals of R?

c) Show that R/M is isomorphic to**Z**/p**Z**. - May 5th 2013, 05:39 PMjohngRe: maximal and prime ideals question
Hi,

Attached is the complete solution:

Attachment 28258