Is there a convention, law or axiom for associate operators when is a lack of brackets? If a have an operator $\circledast:A\times A\rightarrow A$ and $a,b,c\in A$, then the expression
$$a\circledast b\circledast c$$
Can be interpreted only as  $(a\circledast b)\circledast c$ or is possible to interprete it as $a\circledast (b\circledast c)$?
Regardless if $\circledast$ is a associative or nonassociative operator.
And no matter if it's seen by a left-to-right reader (as a japanese person) or a right-to-left reader (as an english person).
 A: If $\circledast$ is not associative then in general 
$$a\circledast (b\circledast c) \neq (a\circledast b)\circledast c$$
so just writing 
$$a\circledast b\circledast c$$
would be ambiguous, unless we follow some convention of right of left associativity. As far as I know, when you see something like $a\circledast b\circledast c$ the operator $\circledast$ is taken to be associative, otherwise brackets would be added. So that means that you can then take $a\circledast (b\circledast c) $ or $(a\circledast b)\circledast c$ because these two are equal by associativity.
A: Even though your answer has already been answered, it's important to notice that your expression doesn't make sense unless
$$
\circledast: A\times A\times A \to A.
$$
In this case, associativity doesn't matter and you can write $a\circledast b\circledast c$.
On the other hand, if your operation is defined as $\circledast:A\times A\to A$, something like $a\circledast b \circledast c$ isn't even defined a priori until you define the associativity.
