Closure operations that induce big Cohen–Macaulay algebras

Research paper by RebeccaR.G.

Indexed on: 31 Oct '17Published on: 01 Aug '17Published in: Journal of Pure and Applied Algebra


We study closure operations over a local domain R that satisfy a set of axioms introduced by Geoffrey Dietz. The existence of a closure operation satisfying the axioms (called a Dietz closure) is equivalent to the existence of a big Cohen–Macaulay module for R. When R is complete and has characteristic p>0<math class="math"><mi is="true">p</mi><mo is="true">&gt;</mo><mn is="true">0</mn></math>, tight closure and plus closure satisfy the axioms.