Let K[X] be the ring of polynomials over the field K and let
f K[X]. Let K[X]/(f) be the quotient
ring by (f). In K[X]/(f) how can I define multiplication by
a scalar in K in order to make K[X]/(f) into a K-vector space?
Thanks for reading.
Thank you for your reply.
I see. And I also see that, with this multiplication, K[X]/(f)
is a K-algebra. My question realy is: is this the only way to define a multiplication by scalar
that makes K[X]/(f) into a K-algebra? Or is it that there are more than one way of building
an K-algebra out of K[X]/(f)?