TENSOR-PRODUCTS AND COMPUTABILITY

We consider the problem of computability in tenser products of modules over a ring. We exhibit a finite local ring A and a pair of A-modules , given explicitly by generators and relations, with the following pro perty. The operations in each module are computable in polynomial time , but equality in their tenser product is undecideable. The constructi on is of interest because it directly embeds Turing machine-like compu tations into the tenser product. We also present sufficient conditions for equality in tenser products to be decideable.