# 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).