I have the set K={a+b sqrt(d) with a,b rational} I know how to show it is a subring, but how do I show it is a subfield? I can show a ring is a field, but is the process same to show a subring is a subfield?
I have the set K={a+b sqrt(d) with a,b rational} I know how to show it is a subring, but how do I show it is a subfield? I can show a ring is a field, but is the process same to show a subring is a subfield?
Thanks
Almost: showing this is a subring and even an integer domain is pretty easy. The tricky thing is to show that any non-zero element has an inverse, but even that is fairly easy. Try it (remember conjugates and stuff).