Matrix versions of real and quaternionic Nullstellensätze

Abstract

Real Nullstellensatz is a classical result from real algebraic geometry. It has recently been extended to quaternionic polynomials by Alon and Paran. The aim of this paper is to extend their quaternionic Nullstellensatz to matrix polynomials. We also obtain an improvement of the real Nullstellensatz for matrix polynomials in the sense that we simplify the definition of a real left ideal. We use the methods from the proof of the matrix version of Hilbert's Nullstellensatz and we obtain their extensions to a mildly non-commutative case and to the real case.

Keywords

algebraična geometrija;izreki o ničlah;polinomi na nekomutativnimi obsegi;matrični kolobarji;kvaternioni;real algebraic geometry;Nullstellensatz;polynomials over division algebras;matrix rings;quaternions;

Data

Language:	English
Year of publishing:	2022
Typology:	1.01 - Original Scientific Article
Organization:	UL FMF - Faculty of Mathematics and Physics
UDC:	512.552
COBISS:	139324931
ISSN:	0021-8693
Views:	45
Downloads:	20
Average score:	0 (0 votes)
Metadata:

Other data

Secondary language:	Slovenian
Secondary keywords:	algebraična geometrija;izreki o ničlah;polinomi nad nekomutativnimi obsegi;matrični kolobarji;kvaternioni;
Type (COBISS):	Article
Pages:	str. 752-772
Issue:	ǂVol. ǂ610
Chronology:	Nov. 2022
DOI:	10.1016/j.jalgebra.2022.06.038
ID:	17890476