 Truncated polynomial ring

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