Let $S⊂Z$ be the set of all integers $n$ such that $gcd(n,10) = 1$.It is a multiplicative set, therefore, we can form the ring of quotients $R=Z[S^-1]$.
Describe the irreducible elements of R.
I'd appreciate help with this. I know that an irreducible element can only be factored such that one of the factors is a unit. Seeing as the elements of $R$ are of the form $a/b$ where $a$ is any integer and $b$ is coprime with $10$. I need to determine which of these elements cannot be factored.
I'm unsure how to proceed.