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In talking about congruence classes modulo a polynomial, my text mentions the following: "... we may think of $F[x]/(m(x))$ as $F[\alpha]$, the set of polynomials with coefficients in $F$ evaluated at the congruence class $\alpha = [x]_{m(x)}$."

So what does $[x]_{m(x)}$ mean? Does it refer to all $b(x)$ such that $b(x) \equiv x \pmod {m(x)}$ ?

Hopefully this question is clear in this brief context...

Thanks in advance!

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What textbook are you using? The more context you provide the more likely you'll receive an optimal answer. – Bill Dubuque May 2 '11 at 13:26
up vote 1 down vote accepted

I believe that,

$\left[ x \right]_{m(x)} = b(x) + \left(m(x)\right)$, where $b(x) \in F[\alpha]$ s.t. $deg(b(x)) < deg(m(x))$

Check here for more notes on Modular Arithmetic and Congruence Classes with Polynomials

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