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/pZ .
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/pZ .