Decompositions of Ideals

New Mexico State University, Las Cruces NM

Investigators

Abstract

The PI will continue her investigations on the decompositions of ideals and how different operations on the ideals interact with the decompositions. The particular operations in the proposal are integral closure, tight closure, adjoints, Rees valuations, symbolic powers, Groebner bases. The PI works in the area of mathematics known as commutative algebra, with applications to the area of algebraic geometry. In particular, there are algebraic constructs that describe geometric objects, such as spheres, cones, cylinders, etc. The (non) "smoothness" as well as many other geometric properties of a geometric object are reflected in the properties of its corresponding algebraic construct, which is useful because the latter is much more susceptible to manipulation. A familiar example might be the prime factorization of integers or polynomials, such as used in cryptography, but in more general situations the corresponding "factorizations" are more complex and highly non-unique.