20 citations · 31 across the 23 of their papers we have counts for
5 papers · 1 filter
The integral closure of a primary ideal is not always primary
Nan Li, Zijia Li, Zhi-Hong Yang +1
In 1936, Krull asked if the integral closure of a primary ideal is still primary. Fifty years later, Huneke partially answered this question by giving a primary polynomial ideal wh…
Extensions of S-Lemma for Noncommutative Polynomials
Feng Guo, Sizhuo Yan, Lihong Zhi
We consider the problem of extending the classical S-lemma from commutative case to noncommutative cases. We show that a symmetric quadratic homogeneous matrix-valued polynomial is…
Sparse sum of Hermitian squares in group algebras of finite groups
Jianting Yang, Ke Ye, Lihong Zhi
Nonnegative elements in group algebras play a central role in harmonic analysis, operator algebras, and computational optimization. This paper investigates sparse sum-of-Hermitian-…
A Vergleichsstellensatz of Strassen's Type for a Noncommutative Preordered Semialgebra through the Semialgebra of its Fractions
Tao Zheng, Lihong Zhi
Preordered semialgebras and semirings are two kinds of algebraic structures occurring in real algebraic geometry frequently and usually play important roles therein. They have many…
Computing sparse Fourier sum of squares on finite abelian groups in quasi-linear time
Jianting Yang, Ke Ye, Lihong Zhi
The problem of verifying the nonnegativity of a function on a finite abelian group is a long-standing challenging problem. The basic theory of representation theory of finite group…