As mentioned in the user6976 answer, there is the idea of development of algebraic geometry to (essentialy) any general algebraic system. This is carried out(following Plotkin's work) by E. Daniyarova, A. Miasnikov, V. Remeslennikov and co-authors in a series of papers.

A more recent survey (2016) of this area, called Universal Algebraic Geometry, of which (non-necessarely associative) algebras is naturally of central interest, is Artem N. Shevlyakov's Lectures notes in universal algebraic geometry.

This survey is very easy to read, and has a very good bibliography ponting out to more specific topics.

As mentioned in the answer by user6976, there is the idea of development of algebraic geometry to (essentialy) any general algebraic system. This is carried out(following Plotkin's work) by E. Daniyarova, A. Miasnikov, V. Remeslennikov and co-authors in a series of papers.

A more recent survey (2016) of this area, called Universal Algebraic Geometry, of which (not necessarily associative) algebras is naturally of central interest, is Artem N. Shevlyakov's Lectures notes in universal algebraic geometry.

This survey is very easy to read, and has a very good bibliography ponting out to more specific topics.