The work of Kim and Roush on questions of decidability in algebra and number theory (Q368679)

This article surveys without proofs the work of K. H. Kim and F. W. Roush in questions of decidability in algebra and number theory. Following topics are touched: -- diophantine undecidability of \({\mathbb C}(t_1, t_2)\), diophantine undecidability over \(p\)-adic function fields, -- diophantine unsolvability for function fields over certain infinite fields of finite characteristic, -- problems equivalent to rational diophantine solvability, -- undecidability of parametric solutions of polynomial equations, -- undecidability of module homomorphisms, -- a decision procedure for certain abelian varieties over function fields, -- double coset decompositions for algebraic groups over \(K[t]\), -- undecidability of isomorphisms of forms over polynomial rings