Abstract Algebra Answers

Find aba -1

where (i) a = (5 , 7 , 9) , b = (1 , 2, 3) (ii) a = (1 , 2,5)(3 , 4) , b = (1 , 4 , 5) .

Find aba -1

where (i) a = (5 , 7 , 9) , b = (1 , 2, 3) (ii) a = (1 , 2,5)(3 , 4) , b = (1 , 4 , 5) .

F ind aba -1 w here (i) a = (5 , 7 , 9) , b = (1 , 2, 3) (ii) a = (1 , 2,5)(3 , 4) , b = (1 , 4 , 5) .

If G is the abelian group of integers in the m apping T: G → G given by T(x ) = x then prove that as an autom orphism

If H and K is subgroup prove H intersection K is subgrop.

[DMe] Define group. Show that the set P3 of all permutations on three symbols 1,2,3 is a finite non-abelian group of order six with respect to permutation multiplication as composition.

if G is the abelian group of integers in the mapping T:G to G given by T(x) = x then prove that as an automorphism

If A,B C are three ideals of a ring R then show that A(BC)=(AB)C

Show that a ring can't be expressed as union of 2 proper ideals but it is possible to express it as a union of three proper ideals

P rove that all real of the form a + b 2 , a; b ∈ Z form s a ring.