I was reading S.Lang's Algebra and it says "Let $ \bar b$ be an element of $A/A_1'$ of period $p^r$, Then there exists a representative $a$ of $\bar b$ in $A$ which also has period $p^r$" in lemma $8.3$.
I couldn't find the definition of the term "representative $a$ of $\bar b$".
ps. I am sorry if my English is bad, I'm not very familiar with it.
By definition, a quotient of a set is a partition into subsets, called congruence classes.
An element of the quotient set is one of these congruence classes. A representative of a class is simply an element of that class.
E.g. $\Bbb Z/2\Bbb Z=\{\bar 0= \text{set of even integers}, \bar 1= \text{set of odd integers}\}$, and a representative of $\bar 0$ is simply any even integer.