Combinatorial Nullstellensatz over division rings

Elad Paran

doi:10.1007/s10801-023-01263-1

Combinatorial Nullstellensatz over division rings

Elad Paran

Mathematics

Open University of Israel

Research output: Contribution to journal › Article › peer-review

Abstract

We extend Alon’s Combinatorial Nullstellensatz from polynomial rings over fields to polynomial rings over division rings and to rings of polynomial functions over centrally finite division algebras. We apply our results to extend classical theorems from additive number theory to the additive theory of division rings, where the size of algebraic sets is measured by their rank in the sense of Lam.

Original language	English
Pages (from-to)	895-911
Number of pages	17
Journal	Journal of Algebraic Combinatorics
Volume	58
Issue number	3
DOIs	https://doi.org/10.1007/s10801-023-01263-1
State	Published - Nov 2023

Keywords

Combinatorial Nullstellensatz
Division rings
Noncommutative ring theory

All Science Journal Classification (ASJC) codes

Algebra and Number Theory
Discrete Mathematics and Combinatorics

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10.1007/s10801-023-01263-1

Cite this

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title = "Combinatorial Nullstellensatz over division rings",

abstract = "We extend Alon{\textquoteright}s Combinatorial Nullstellensatz from polynomial rings over fields to polynomial rings over division rings and to rings of polynomial functions over centrally finite division algebras. We apply our results to extend classical theorems from additive number theory to the additive theory of division rings, where the size of algebraic sets is measured by their rank in the sense of Lam.",

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doi = "10.1007/s10801-023-01263-1",

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AB - We extend Alon’s Combinatorial Nullstellensatz from polynomial rings over fields to polynomial rings over division rings and to rings of polynomial functions over centrally finite division algebras. We apply our results to extend classical theorems from additive number theory to the additive theory of division rings, where the size of algebraic sets is measured by their rank in the sense of Lam.

KW - Combinatorial Nullstellensatz

KW - Division rings

KW - Noncommutative ring theory

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DO - 10.1007/s10801-023-01263-1

M3 - مقالة

SN - 0925-9899

VL - 58

SP - 895

EP - 911

JO - Journal of Algebraic Combinatorics

JF - Journal of Algebraic Combinatorics

IS - 3

ER -

Combinatorial Nullstellensatz over division rings

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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