Images of Multilinear Polynomials with a Standard-Polynomial Unit Specialization
Year: 2026
Type: preprint
Abstract: For r = 3, 4, 5, consider an ordinary multilinear polynomial f(Y, X₁, …, X₂ᵣ) whose specialization at Y = I is a nonzero scalar multiple of the standard polynomial s₂ᵣ. Over an algebraically closed field K of characteristic zero, we prove that for every n ≥ r + 1 the set of its individual values on Mₙ(K) is slₙ(K) if its trace vanishes identically, and Mₙ(K) otherwise. This includes arbitrary proper perturbations of s₇, s₉, s₁₁. The proof combines exact standard-polynomial core constructions, additive size transfer, and a mixed-frame compatibility lemma with a local lifting criterion of Pan.
Author: Miah, Y. T.
Language: English
Topic: Rings, Modules, and Algebras
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7225598142