Truncated polynomial ring
= Truncated polynomial ring
{title2=$R[Y]/(Y^n)$}
For a <commutative ring> $R$ and $n\geq1$, this <quotient ring> imposes $Y^n=0$. Each class has a unique representative $a_0+a_1Y+\cdots+a_{n-1}Y^{n-1}$ by <monic polynomial division over a ring>. Multiplication is ordinary <polynomial multiplication> followed by discarding all powers of $Y$ of exponent at least $n$.