XXXXXXX (XXXXXXXX SOLVE STEP BY STEP SOLVE STEP BY STEP PLEASE VVVVVVVVVVVVVVVVVVVV ᏙᏙᏙᏙᏙᏙᏙᏙᏙᏙᏙᏙᏙᏙᏙᏙᏙᏙᏙᏙᏙᏙᏙᏙᏙᏙ Let K be

[answerhappygod]

1 (38.43 KiB) Viewed 18 times

XXXXXXX (XXXXXXXX SOLVE STEP BY STEP SOLVE STEP BY STEP PLEASE VVVVVVVVVVVVVVVVVVVV ᏙᏙᏙᏙᏙᏙᏙᏙᏙᏙᏙᏙᏙᏙᏙᏙᏙᏙᏙᏙᏙᏙᏙᏙᏙᏙ Let K be a field and consider the ring of polynomials A = K[r]. a) Prove that if M is an A-module, then it is a K-vector space and that multiplication by x defines a K-Linear operator T on M. b) Show that if V is a K-vector space and T is a linear operator on V, then T defines an A-module structure on V C) Show that, under the above correspondences, the submodules of M correspond to invariant vector subspaces under the operator T