MHB Abstract algebra: i need examples of ...

[nweissma]

please offer me examples of: a) 3 vector spaces over the same field; and b) the same vector space over 3 fields.

 

[HOI]

The space of all vectors of tne form <a, b>, where a and b are real number, over the real numbers.
The space or all vectors of the form <a, b, c> over the real numbers.
The space of all polynomials of degree 3 or less over the real numbers.

Since the underlying field is part of the definition of a vector space, I'm not sure I would agree that you can have the same vector space over different fields.

However, if I were required to answer such a question (!), I would say the vector space of all complex numbers over the field of
the rational numbers
the real numbers
the complex numbers.