Notation in quotient rings

I was reading my lecture notes and the symbol $/$ is used commonly but it is not really defined anywhere, so I was wondering if someone could explain it to me.

For example, in the definition of a quotient ring from an ideal

$$R/I = \{ a + I : a \in R \}$$

where $I$ is an ideal and $R$ is a ring. What exactly does the forward slash mean?

• It's a notation denoting "quotient". – Lord Shark the Unknown Mar 2 '18 at 18:22

The equation $$R/I = \{ a + I : a \in R \}$$ is the definition of the notation $R/I$. So you're not expected to know what the forward slash means before this definition: this is telling you what it means!
• , although a definition without an explanation in words is not so valuable. I would have told the students to make sure that they included in their notes some words about $R/I$ being the set of all cosets of $I$. – Lubin Mar 3 '18 at 0:37