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



Literature on the polynomials and equations, in structures with zero-divisors
For **associative algebras**, as your required, see Plotkin, *Algebras with the same (algebraic) geometry*, Israel J. Math., 96 (2) (1996), 511–522.


This is, being more precise, part of this nice relatively new field of Universal Algebraic Geometry which discuss such things.


For a survey I recommend A. Shevlyakov, *Lectures notes in universal algebraic geometry*, <https://arxiv.org/abs/1601.02743>.




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**EDIT** depending on the kind of question you are interested in, pherhaps the theory of (associative) PI-algebras might be also interesting. For this I recommend V. Drensky's *Free Algebras and PI-algebras*.


