Prabhupada posted an Question
May 13, 2020 • 18:34 pm 30 points
  • IIT JAM
  • Mathematics (MA)

If a vectorspace is countable and field is also countable, then does it imply that the vectorspace is finitely generated vector space?

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  • Pulkit khandelwal Best Answer

    Take field of all rational numbers and consider vectorspace of all polynomials witch coefficien is rational number. Clearly both are countable but vectorspace os not finitely generated as its basis is {x^n | n belongs to natural number} so given statement is false

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