If $R$ is a unital associtaitve commutative ring, then can any $R$-algebra $A$ may be filtered as $A_0:=A$ and $A_{i+1}:=(A_i,A_i)$ where $(-,-)$ is the commutator of $A$ with respect to $A$'s multiplication?
Moreover, is so then I'm assuming that $A$ may be graded as $\bigoplus A_i$?