[代數] modules Galois
1.prove that minimal polynomial of Anxn over F(characteristic zero) and the
characteristic polynomial have the same set of irreducible factors.
2.let f:Z^3->Z^3 be the homomorphism of free Z-module Z^3 to itself given by
multiplication of the matrix B.show that f(Z^3) is a free Z-moduke of rank 2.
B= (1 2 3)
(2 3 4)
(3 4 5)
3.compute the Galois group of the polynomial (x^2+1)(x^3-x^2-2x+1) over Q.
4.let f<Q[x] irr poly, deg(f)=4,show that if its Galois group is C4,then
its discriminant must be a positive nonsquare rational munber.
thanks
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