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Abstract Algebra
The characteristic of a finite field is zero. Is this statement true or false, justify your answer.
Abstract Algebra
If a ring has a unit, then it has only one unit. Is this statement true or false ,justify your answer.
Abstract Algebra
If σ ∈ Sn (n ≥ 3 ) is a product of an even number of disjoint cycles, then sign (σ) = 1. Is this statement true or false, justify your answer.
Abstract Algebra
If R is a ring and I is an ideal of R , then xr = rx ∀ x ∈ I and r ∈ R . Is this statement true or false, justify your answer .
Abstract Algebra
Every element of Sn has order at most n . Is this statement true or false, justify your answer.
Abstract Algebra
If G is a group and H∆G , then | G : H |= 2 . Is this statement true or false, justify your answer.
Abstract Algebra
If G is an abelian group, then G is cyclic. Is this statement true or false . Also justify your answer.
Abstract Algebra
If G1 and G2 are groups, and f : G1→G2 is a group homomorphism, then
o(G1) = o( G2). Is the statement true or false ? Also justify.
o(G1) = o( G2). Is the statement true or false ? Also justify.
Abstract Algebra
show that the Galois groups of x^4 -1 and x^2 - x +1 over Q are isomorphic
Abstract Algebra
Show that there are infinitely many values of a for which x7+15x2-30x+a is irreducible in Q[x].
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#340153 on Dec 2023
#340153 on Dec 2023