Linear equivalence of ideal topologies (Q1581836)

Let \(P\) be a prime ideal in a commutative Noetherian ring \(R\). The main result of the paper is the following: If the \(P\)-adic and \(P\)-symbolic topologies on \(R\) are equivalent, then the two topologies are linearly equivalent. In the proof a main tool is the reduction to the hypersurface case. The paper ends with explicit calculations of linear equivalence.