# Notation help

• Mar 24th 2011, 08:45 AM
Josh146
Notation help
I know the definition of a field but I haven't really studied much algebra. Can someone tell me what this means:

\$\displaystyle \mathbb{F}_2[x,y]/(x^r,y^s)\$

I know it involves a 2-element field but that's about it.
• Mar 24th 2011, 09:56 AM
Deveno
it's a quotient ring. the "main ring" is the ring of polynomials in x and y, with coefficients in the 2-element field F2 = {0,1}. that ring is being factored via the ideal generated by two polynomials x^r and y^s (that is, any polynomial of the form p(x,y)x^r + q(x,y)y^s is treated as if it was 0, so basically this knocks off all powers of x higher than r-1, and all powers of y higher than s-1).
• Mar 24th 2011, 09:58 AM
FernandoRevilla
It is the quotient ring \$\displaystyle R/I\$ . In this case \$\displaystyle R\$ is the ring \$\displaystyle \mathbb{F}_2[x,y]\$ and \$\displaystyle I=(x^r.y^s)\$ the ideal generated by \$\displaystyle x^r\$ and \$\displaystyle y^s\$ .

Edited: Sorry, I didn't see Deveno's post.