On bilinear maps on matrices with applications to commutativity preserversBrešar, Matej (Avtor) Šemrl, Peter (Avtor) mathematicsmatrix algebracentral simple algebrafunctional identitynonassociative productLie-admissible algebracommutativity preserving mapLet ▫$M_n$▫ be the algebra of all ▫$n times n$▫ matrices over a commutative unital ring ▫$mathcal{C}$▫, and let ▫$mathcal{L}$▫ be a ▫$mathcal{C}$▫-module. Various characterizations of bilinear maps ▫${,.,,,.,}: M_n times M_n to mathcal{L}$▫ with the property that ▫${x,y} = 0$▫ whenever ▫$x$▫ any ▫$y$▫ commute are given. As the main application of this result we obtain the definitive solution of the problem of describing (not necessarily bijective) commutativity preserving linear maps from ▫$M_n$▫ into ▫$M_n$▫ for the case where ▫$mathcal{C}$▫ is an arbitrary field; moreover, this description is valid in every finite dimensional central simple algebra.Elsevier20062015-07-10 14:54:27Znanstveno delo51552sl