$\DeclareMathOperator{\charac}{char}$I am going to quickly recall the notion of approximate roots of polynomials due to Abhyankar and Moh, as stated in [Russell, 1980], and going to add a few remarks on the case that the corresponding exponent is not invertible. Let $A$ be a ring (with an identity) and $f \in A[x]$, where $x$ is… Continue reading Approximate roots of polynomials – part 1