# Closure operations that induce big Cohen–Macaulay modules and classification of singularities

Research paper by Rebecca R.G.

Indexed on: 08 Oct '16Published on: 20 Aug '16Published in: Journal of Algebra

#### Abstract

Geoffrey Dietz introduced a set of axioms for a closure operation on a complete local domain R   so that the existence of such a closure operation is equivalent to the existence of a big Cohen–Macaulay module. These closure operations are called Dietz closures. In complete rings of characteristic p>0p>0, tight closure and plus closure satisfy the axioms.