O jordanovyh idealah i podmoduljah: algebraičeskij i analitičeskij aspekty
Brešar, Matej ; Kissin, Edward ; Shulman, Victor S.
Naj bo ▫$A$▫ algebra in naj bo ▫$X$▫ ▫$\mathcal{A}$▫-bimodul. Linearni podprostor ▫$Y \subset X$▫ imenujemo jordanski ▫$\mathcal{A}$▫-podmodul, če velja ▫$Ay + yA \in Y$▫ za vse $A \in \mathcal{A}$ ...in vse ▫$y\in Y$▫ (za ▫$X = \mathcal{A}$▫ to sovpada s pojmom jordanskega ideala). Obravnani so pogoji, pod katerimi so jordanski podmoduli (asociativni) podmoduli. Splošni kriteriji so podani tako v algebraičnem kontekstu kot v kontekstu Banacahovih bimodulov. Obravnavani so tudi simetrični normirani jordanski podmoduli nad ▫$C^\ast$▫-algebrami. Izkaže se, da obstajajo ▫$C^\ast$▫-algebre, v katerih niso vsi jordanski ideali (asociativni) ideali.
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