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On bilinear maps on matrices with applications to commutativity preservers
Brešar, Matej ; Šemrl, Peter
Naj bo ▫$M_n$▫ algebra vseh ▫$n \times n$▫ matrik nad komutativnim enotskim kolobarjem ▫$\mathcal{C}$▫, and naj bo ▫$\mathcal{L}$▫ modul nad ▫$\mathcal{C}$▫. Podane so različne karakterizacije ...bilinearnih preslikav ▫$\{\,.\,,\,.\,\}: M_n \times M_n \to \mathcal{L}$▫ z lastnostjo, da je ▫$\{x,y\} = 0$▫, kadarkoli ▫$x$▫ in ▫$y$▫ komutirata. Kot glavno aplikacijo dobimo dokončno rešitev problema opisa (ne nujno bijektivnih) linearnih ohranjevalcev komutativnosti iz ▫$M_n$▫ v ▫$M_n$▫ za primer, ko je ▫$\mathcal{C}$▫ poljubno polje; še več, enak opis velja v vsaki končno razsežni centralni enostavni algebri.
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