Fundamental Results on $s$-Closures
- Resource Type
- Working Paper
- Authors
- Taylor, William D.
- Source
- Subject
- Mathematics - Commutative Algebra
13A35 (Primary) 13A02, 13B22, 13H15 (Secondary)
- Language
This paper establishes the fundamental properties of the $s$-closures, a recently introduced family of closure operations on ideals of rings of positive characteristic. The behavior of the $s$-closure of homogeneous ideals in graded rings is studied, and criteria are given for when the $s$-closure of an ideal can be described exactly in terms of its tight closure and rational powers. Sufficient conditions are established for the weak $s$-closure to equal to the $s$-closure. A generalization of the Briancon-Skoda theorem is given which compares any two different $s$-closures applied to powers of the same ideal.
Comment: 10 pages