this is abstract algebra Let M be a Q[x]-module which is ﬁnite-dimensional as a vector space....

this is abstract algebra

Let M be a Q[x]-module which is ﬁnite-dimensional as a vector space. What is its torsion submodule?

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Colby Messinger answered 6 months ago

this is abstract algebra Let M be a Q[x]-module which is ﬁnite-dimensional as a vector space....

this is abstract algebra Let M be a Q[x]-module which is ﬁnite-dimensional as a vector space. What is its torsion submodule?

1. Let ? be a finite dimensional vector space with basis {?1,...,??} and ? ∈ L(?)....

1. Let ? be a finite dimensional vector space with basis {?1,...,??} and ? ∈ L(?). Show the following are equivalent: (a) The matrix for ? is upper triangular. (b) ?(??) ∈ Span(?1,...,??) for all ?. (c) Span(?1,...,??) is ?-invariant for all ?. please also explain for (a)->(b) why are all the c coefficients 0 for all i>k? and why T(vk) in the span of (v1,.....,vk)? i need help understanding this.

Let V be a finite dimensional vector space over R. If S is a set of...

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Let T be a linear operator on a finite-dimensional complex vector space V . Prove that T is diagonalizable if and only if for every λ ∈ C, we have N(T − λIV ) = N((T − λIV )2).

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(abstract algebra) Let F be a field. Suppose f(x), g(x), h(x) ∈ F[x]. Show that the...

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Let V be the 3-dimensional vector space of all polynomials of order less than or equal...

Let V be the 3-dimensional vector space of all polynomials of order less than or equal to 2 with real coeﬃcients. (a) Show that the function B: V ×V →R given by B(f,g) = f(−1)g(−1) + f(0)g(0) + f(1)g(1) is an inner product and write out its Gram matrix with respect to the basis (1,t,t2). DO NOT COPY YOUR SOLUTION FROM OTHER SOLUTIONS

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this is abstract algebra Let M be a Q[x]-module which is ﬁnite-dimensional as a vector space....

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