A constructive proof of the general Nullstellensatz for Jacobson rings

We give a constructive proof of the general Nullstellensatz: a univariate polynomial ring over a commutative Jacobson ring is Jacobson. This theorem implies that every finitely generated algebra over a zero-dimensional ring or the ring of integers is Jacobson, which has been an open problem in constructive algebra. We also prove a variant of the general Nullstellensatz for finitely Jacobson rings.

💡 Research Summary

This paper presents a fully constructive proof of the General Nullstellensatz, namely that if a commutative ring A is Jacobson then the polynomial ring A