Hi:

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.

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- October 17th 2009, 05:40 AMENRIQUESTEFANINIMultiplication by scalar in K[X]/(f)
Hi:

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. - October 17th 2009, 09:59 AMtonio
- October 17th 2009, 04:50 PMENRIQUESTEFANINI
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)?

Enrique. - October 17th 2009, 07:47 PMtonio
- October 18th 2009, 01:44 AMENRIQUESTEFANINI