The perfect Nullstellensatz just got more perfect
After giving a talk about the perfect Nullstellensatz (the commutative free Nullstellensatz) at the Technion Math department’s pizza and beer seminar, I had a revelation: I think it holds over other fields as well, not just over the complex numbers! (And in particular, contrary to what I thought before, it holds over the reals. It seems to hold over other fields as well).
To explain, I will need some notation.
Let be a field. We write
– the algebra of all polynomials in
(commuting) variables over the field
.