Abstract Algebra Answers

Check whether x^5+9x^4+12x^2+6 is reducible over Q.

Let S = { a + ib / a , b ∈ Z ,b is even } Show that S is a
subring of Z[i] , but not an ideal of Z[i]

Show that polynomial x⁵=9x+3 Is not solvable by radicals over.

find all of the motions of a rhombus, abcd, define each motion as a permutation (and write each as a product of disjoint cycles), find the composition table (using permutations), and determine if the set of motions under composition is a group.

Check whether x^5+9x^4+12x^2+6 is reducible over Q.

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>