#1)

Is Z an ideal in Q?

Z는 Q의 subring 맞고,

for any p/q in Q, q in Z and q*p/q=p in Z

So, Yes.


#2)

Let F be the ring of all functions from R to R, and let C be the subring of F consisting of all the constant functions in F.

Is C an ideal in F?

For any f of F, consider 0 in C

Then 0*f=0 in C

So, Yes.


#3)

Find all ideals in Z.

For any a in Z, consider nb in nZ

Then a*nb in nZ

So, nZ is an ideal of Z


And consider {0}

then a*0 in {0}

So, {0} is an ideal of Z

그리고.. 더 있을까요?


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