Results on undecidability of isomorphism of forms over polynomial rings

Abstract

We show the undecidability of the question of isomorphism of forms over a polynomial ring R[t 1 , . . . , tn], assuming a hypothesis about units in certain quaternion rings. Assuming this, it follows that isomorphisms of modules, and of affine algebraic varieties over R are undecidable.

The Work of Kim and Roush on Questions of Decidability in Algebra and Number Theory

“…In [11] Kim and Roush prove a conditional undecidability result for the isomorphism of forms over certain polynomial rings. This is applied to related decision problems.…”