A quotient of a polynomial ring – math.stackexchange.com

Let $\mathbb{F}_2$ be the field with $2$ elements. Can we write the following quotient of the ring $\mathbb{F}_2[x,y]$ simpler? $$\frac{\mathbb{F}_2[x,y]}{\langle x^{2^a}-1,y^{2^b}-1\rangle}$$ ...

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