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Abstract Algebra
Prove that (R^5)/R ~_ R^4 as rings
Abstract Algebra
p and Q are subgroups of a group G and o(P) and o(Q) relatively prime prove that p intersection Q=e,e belonge to G
Abstract Algebra
b) Let
σ =
3 4 5 2 1
1 2 3 4 5
and
τ =
5 3 2 4 1
1 2 3 4 5
in . S7
Write στ as a product
of disjoint permutations.
Further, is στ even? Why, or why not?
σ =
3 4 5 2 1
1 2 3 4 5
and
τ =
5 3 2 4 1
1 2 3 4 5
in . S7
Write στ as a product
of disjoint permutations.
Further, is στ even? Why, or why not?
Abstract Algebra
Which of the following statements are true? Give reasons for your answers, in the form
of a short proof or a counterexample.
i) ( ) M3 Z has no nilpotent elements.
of a short proof or a counterexample.
i) ( ) M3 Z has no nilpotent elements.
Abstract Algebra
Show that z(sqrt-2) is non ufd
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?
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?
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
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
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#340153 on Dec 2023
#340153 on Dec 2023