Consider the following rings:

$A=\mathbb{C}\lbrace x,y,u \rbrace /(xy+x^3,y^2,xy^2+x^5) \ $ and

$B=\mathbb{C}\lbrace x,y,u \rbrace /(xy+x^3,y^2+ux^4,xy^2+x^5)$

There is an isomorphism of $\mathbb{C}$-algebras between $A$ and $B$?

Here $\mathbb{C}\lbrace x,y,u \rbrace$ denotes the formal series ring. I'm trying to prove that there is an isomorphism between $A$ and $B$, but I suspect that this isomorphism can not exist. Furthermore, I would like to see if there is at least one morphism between $A$ and $B$ or maybe between $B$ and $A$?

I would be happy with any suggestions.