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Let S={a+ib/a,b element of Z,b is even} show that S is a subring of Z[i],but not an ideal of Z[i]
Prove that Z[√2]={a+b√2;a,b element of Z} is a ring under the ordinary addition and multiplication
Find the number of elements of order 9 in Z3 (product ) Z9
Find the order of all elements of S3
In Z12,find the subgroups <2>,<3>,<4>,<5> and <6>
On Q/{-1} define * by a*b=a+b+an for all a,b element of Q/{-1} show that (Q/{-1},*) is an abelian group
Let G={3^n;n element of Z} prove that (G,•)

is an abelian group
Homomorphism
Show that the polynomial
X5=9x + 3
Is not solvable by radicals over
Show that the polynomial
X5=9x + 3
Is not solvable by radicals over
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