7 citations · 23 across the 5 of their papers we have counts for
7 papers
Tensor-Multinomial Sums of Ideals: Primary Decompositions and Persistence of Associated Primes
Irena Swanson, Robert M. Walker
Given a polynomial ring over a field and proper ideals and whose generating sets involve disjoint variables, we determine how to embed the associated primes of each pow…
Counting Roots of Polynomials over
Trajan Hammonds, Jeremy Johnson, Angela Patini +1
Until recently, the only known method of finding the roots of polynomials over prime power rings, other than fields, was brute force. One reason for this is the lack of a division…
Uniform Symbolic Topologies in Normal Toric Rings
Robert M. Walker
Given a normal toric algebra , we compute a uniform integer such that the symbolic power for all and all monomial primes . We…
Uniform Symbolic Topologies via Multinomial Expansions
Robert M. Walker
When does a Noetherian commutative ring have uniform symbolic topologies on primes--read, when does there exist an integer such that the symbolic power $P^{(Dr)} \subsete…
Uniform Harbourne-Huneke Bounds via Flat Extensions
Robert M. Walker
Over an arbitrary field , Harbourne conjectured that for all and all homogeneous ideals in $S = \mathbb{F} [\mathbb{P}^N] =…
Rational Singularities and Uniform Symbolic Topologies
Robert M. Walker
Take any normal Noetherian domain, either local or -graded over a field. We study the question of when satisfies the uniform symbolic topology p…