Simple rings and degree maps
For an extension $A/B$ of neither necessarily associative nor necessarily unital rings, we investigate the connection between simplicity of $A$ with a property that we call $A$-simplicity of $B$. By this we mean that there is no non-trivial ideal $I$ of $B$ being $A$-invariant, that is satisfying $AI \subseteq IA$. We show that $A$-simplicity of $B$ is a necessary condition for simplicity of $A$ f