20.500.12556/RUL-144094 Matrix versions of Real and Quaternionic Nullstellensätze 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. Real Algebraic Geometry Nullstellensatz polynomials over division algebras matrix rings quaternions algebraična geometrija izreki o ničlah polinomi nad nekomutativnimi obsegi matrični kolobarji kvaternioni true false true Angleški jezik Slovenski jezik Članek v reviji 2023-01-31 13:31:10 2023-01-31 13:31:12 2023-02-13 10:03:39 0000-00-00 00:00:00 2022 0 0 Str. 752-772 Vol. 610 Nov. 2022 0000-00-00 Zaloznikova Objavljeno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 512.552 0021-8693 10.1016/j.jalgebra.2022.06.038 139324931 1-s2.0-S0021869322003659-main.pdf 1-s2.0-S0021869322003659-main.pdf 1 E50813B415D222B3BD96B6323A991F4C 08c8b1f98d03634545fde572ee3300b809241e25b415ae9641d3578a8c19d44b 20539094-a163-11ed-9c94-00155dcfd717 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=166231 https://www.sciencedirect.com/science/article/pii/S0021869322003659 1 dffd97ea-a162-11ed-9c94-00155dcfd717 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=166230 Fakulteta za matematiko in fiziko 0 0 0