Commutative algebra and algebraic geometry form a deeply interwoven field that investigates the structure of polynomial rings, their ideals, and the geometric objects defined by these algebraic sets.

David Eisenbud, Irena Peeva, Bernd Sturmfels, Non-Commutative Gröbner Bases for Commutative Algebras, Proceedings of the American Mathematical Society, Vol. 126, No ...

We present Bäcklund transformations for the non-commutative anti-self-dual Yang-Mills equation where the gauge group is G = GL(2), and use it to generate a series of exact solutions from a simple seed ...