Ordinary commutative algebraic geometry is based on commutative polynomial algebras over an algebraically closed field $k$. Here we make a natural generalization to matrix polynomial $k$-algebras which are non-commutative coordinate rings of non-commutative varieties.
"Introduction to Non Commutative Algebraic Geometry." J. Phys. Math. 6 (1) 1 - 3, 2015. https://doi.org/10.4172/2090-0902.1000133