Irreducible polynomial in Ring-LWE
The cited paper, as well as the theorem of R-LWE in that paper only requires $f$ to be irreducible over the rationals. For this requirement one usually uses $f = x^n+1$ with $n$ a power of $2$. This polynomial is reducible modulo $q$ but it is okay for the proof to go through.  

The cited paper suggested to use cyclotomic polynomial $\phi_n = 1+x+x^2+...+x^{n-1}$ with $n$ prime. This polynomial is irreducible over $Z$. For some prime $q$, it is also irreducible over $Z_q$. 

Ex:
$n = 11$, $q=17$, 
$\phi_n = x^{10} + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1$ is irreducible mod $q$.