Abstract Algebra

Let a = (1 2 3 4 5
3 4 5 2 1) and b =(1 2 3 4 5
5 3 2 4 1) in S7. Write ab as a product of disjoint permutations. Further, is ab even? Why, or why not?

Abstract Algebra

Is R = {[a a+b
a+b b ] |a,b belongs to Z} a subring of M2(Z)? Why or why not?

Abstract Algebra

Let a = (3 4 5 2 1) and b = (5 3 2 4 1) in S7. Write ab as a product of disjoint permutations. Further, is ab even? Why or why not?

Abstract Algebra

Find the permutation in S_4such that 1→3, 2 2→1, 3→2.

Abstract Algebra

There are the permutations σ=(123), τ=(12). Calculate σ(τ)=τσ (applying \tauτ first and then applying \sigmaσ)
Find the order of the element 2in the group (Z_6,+)
Find the element which belongs to the ring Z_2[x] /x^2+x+1
Let the order of element aa in the finite group be 20. Find the order of element a^6

Abstract Algebra

Find the permutation in S_4
such that 1→3, 2 12→1, 23→2.

Abstract Algebra

Calculate 2+2 in Z_3

Abstract Algebra

modules which are neither Noetherian nor Artinian.is it true of false.if it is one them then give proof

Abstract Algebra

Why zero ring is artinian as well as noetherian?

Abstract Algebra

A Minimal Sub-Module is always Simple ?