The <localization of a ring> $S^{-1}R$ consists of pairs $(r,s)\in R\times S$ modulo
$$
(r,s)\sim(r',s')
\quad\Longleftrightarrow\quad
u(s'r-sr')=0
$$
for some $u\in S$. Addition and multiplication are
$$
\frac rs+\frac{r'}{s'}=\frac{rs'+r's}{ss'},
\qquad
\frac rs\frac{r'}{s'}=\frac{rr'}{ss'}.
$$

Solution

Past exam of the mathematics course of the University of Cambridge / 2021 / iii / Paper 101 / 2 / a / Solution

 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2021/iii/paper-101/2/a/solution