I need literature about zeroes of polynomials and equation resolution in associative algebraic structures with zero-divisors, but I am having difficulties to find it.

For example, there is literature in the resolution of quadratic(and remarks on other degrees) in quaternions and split-quaternions.

It seems that search engines do something with the keyword zero, that has two meanings in this context, this is, zero-divisor and zeroes of the polynomials.

So far I do not find ways to more concrete examples. It would be fine also, algebraic literature ( as opposed to specific examples )

Thanks in advance