The short exact order of the algebras implies the bimodule structure

I have read a statement in "Algebraic Operads" that I do not understand:

To let $$ 0 rightarrow M rightarrow A & # 39; rightarrow A rightarrow 0 $$

Let be a short exact sequence of algebras, so that the product in M ​​is 0. Then M is a bimodule over A.

When we call $ i $ and $ p $ the second and third arrows are each injection and surjection and then $ A & # 39; sim A oplus M $, But I do not see how M inherits a Bimodul structure (or even says left module).