I'm looking for a reference that treats basic module theory over non-associative rings, the isomorphism theorems and so on. I imagine the theory is known, but have not been able to find a reference.


Edit: Let $R$ be a non-associative ring. By a left $R$-module (similarly for a right $R$-module), I mean an abelian group (M,+) and an operation $\cdot\colon R\times M\to M$, such that for all $r\_1,r\_2\in R$ and all $m\_1,m\_2\in M$, the following hold:


1. $(r\_1+r\_2)\cdot m\_1 = r\_1\cdot m\_1 + r\_2\cdot m\_1$,
2. $r\_1\cdot(m\_1+m\_2) = r\_1\cdot m\_1 + r\_1\cdot m\_2$,
3. $1\cdot m\_1 = m\_1$ if $R$ is unital.



Non-associative module theory
A Google search of this term brings a number of references, did you try it? 


In any case, a very obvious relevant reference is the old paper of Osborn called [Modules over nonassociative rings](https://www.tandfonline.com/doi/abs/10.1080/00927877808822293?journalCode=lagb20). 


More recent works define modules over any kind of algebras using the language of operads, but I am not sure that this is what you want since you did not indicate your background and the research area you are coming from. 


