What type of study is this?

This is a Quantitative Study study.

October 10, 2025Open Access

A Unified Solution Formula for Polynomial Equations in Noncommutative Operator Algebras via Differential-Combinatorial Methods

Key Points

A comprehensive framework addresses degree-n polynomial equations in noncommutative operator algebras.
This method constructs a noncommutative operator differential-algebraic closure incorporating critical values and roots.
The closure is closed under p-th roots extraction via holomorphic functional calculus and solving polynomial equations.
Implications may extend to new methods in resolving algebraic equations across diverse operator systems.

Abstract

This paper establishes a comprehensive framework for solving degree-npolynomial equations P(x) = 0 in unital noncommutative operator algebras, including C*-algebras, von Neumann algebras, and general operator systems. We construct a noncommutative operator differential-algebraic closure that extends the coefficient algebra by adjoining critical values of P, all roots of unity, and is closed under the extraction of p-th roots via holomorphic functional calculus and under solving polynomial equations with ordered noncommutative coefficients.

Read Full Paperexternally

Bookmark

View Full Paper

Cite This Study

Liu et al. (Wed,) studied this question.

synapsesocial.com/papers/68e861a57ef2f04ca37e4552 https://doi.org/https://doi.org/10.22541/au.175994530.00057479/v1