TY - JOUR
T1 - Combinatorial Nullstellensatz over division rings
AU - Paran, Elad
N1 - Publisher Copyright:
© 2023, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.
PY - 2023/11
Y1 - 2023/11
N2 - 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.
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
UR - http://www.scopus.com/inward/record.url?scp=85171830424&partnerID=8YFLogxK
U2 - 10.1007/s10801-023-01263-1
DO - 10.1007/s10801-023-01263-1
M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???
AN - SCOPUS:85171830424
SN - 0925-9899
VL - 58
SP - 895
EP - 911
JO - Journal of Algebraic Combinatorics
JF - Journal of Algebraic Combinatorics
IS - 3
ER -