20.500.12556/DiRROS-28954 Left Jacobson rings We say that a ring is strongly (resp. weakly) left Jacobson if every semiprime (resp. prime) left ideal is an intersection of maximal left ideals. There exist Jacobson rings that are not weakly left Jacobson, e.g. the Weyl algebra. Our main result is the following one-sided noncommutative Nullstellensatz: For any finite-dimensional ${\mathbb F}$-algebra ${\mathbb A}$ the ring ${\mathbb A}[x_1, \ldots,x_n]$ of polynomials with coefficients in ${\mathbb A}$ is strongly left Jacobson and every maximal left ideal of ${\mathbb A}[x_1, \ldots,x_n]$ has finite codimension. We also prove that an Azumaya algebra is strongly left Jacobson iff its center is Jacobson and that an algebra that is a finitely generated module over its center is weakly left Jacobson iff it is Jacobson. Nullstellensatz noncommutative geometry maximal left ideals Jacobson ring Azumaya algebra Weyl algebra true false true Angleški jezik Ni določen Neznano 2026-04-14 14:31:09 2026-04-14 14:31:09 2026-04-15 03:57:41 0000-00-00 00:00:00 2026 0 0 str. 453-472 Vol. 698 Jul. 2026 0000-00-00 Zaloznikova Objavljeno NiDoloceno 0000-00-00 0000-00-00 2026-07-01 512 0021-8693 10.1016/j.jalgebra.2026.03.002 275191043 1-s2.0-S0021869326001341-main.pdf 1-s2.0-S0021869326001341-main.pdf 1 2312A7BB8C9874A72E1C083CFD5E28A0 9249969e88b1310288e3e83890bd812b57d4e3bc5e4064242164ccc11b21d4e7 4d940c50-37fe-11f1-9cc3-001a4af901a5 https://dirros.openscience.si/Dokument.php?lang=slv&id=43195 https://www.sciencedirect.com/science/article/pii/S0021869326001341 1 d3130b59-37fd-11f1-9cc3-001a4af901a5 https://dirros.openscience.si/Dokument.php?lang=slv&id=43192 Inštitut za matematiko, fiziko in mehaniko 0 0 0