I have come across the terminology $\mathbb{Z}[X] \stackrel{\mathrm{quot.}}{\to} \mathbb{Z}$ where $\mathbb{Z}[X]$ is the ring of integer polynomials in $\mathbb{Z}$
I am wondering what this quotient map is. From wikipedia: "..given a (not necessarily commutative) ring $A$ containing $K$ and an element $a$ of $A$ that commutes with all elements of $K$, there is a unique ring homomorphism from the polynomial ring $K[X] \to A$ that maps $X$ to $a$:
$\phi: K[X]\to A, \quad \phi(X)=a.$
Edit: So perhaps there is no 'cannoical' map for the question? For what it is worth, I am trying to calculate homology of $0\to R \stackrel{x}{\to} R \stackrel{\mathrm{quot.}}{\to} \mathbb{Z} \to 0$ where $R = \mathbb{Z}[x]$