Two results concerning symmetric be-derivations on prime ringsVukman, Joso (Avtor) matematikaasociativni kolobarji in algebrekolobarprakolobarodvajanjesimetrično bi-odvajanjemathematicsassociative rings and algebrasringprime ringderivationsymmetric bi-derivationLet ▫$R$▫ be a ring. A bi-additive symmetric mapping ▫$D(.,.): R times R to R$▫ is called a symmetric bi-derivation if, for any fixed ▫$y in R$▫, the mapping ▫$x mapsto D(x,y)$▫ is a derivation. The purpose of this paper is to prove two results concerning symmetric bi-derivations on prime rings. The first result states that, if ▫$D_1$▫ and ▫$D_2$▫ are symmetric bi-derivations on a prime ring of characteristic different from two and three such that ▫$D_1(x,x)D_2(x,x) = 0$▫ holds for all ▫$x in R$▫, then either ▫$D_1 = 0$▫ or ▫$D_2 = 0$▫. The second result proves that the existence of a nonzero symmetric bi-derivation on a prime ring of characteristic different from two and three, such that ▫$[[D(x,x),x],x] in Z(R)$▫ holds for all ▫$x in R$▫, where ▫$Z(R)$▫ denotes the center of ▫$R$▫, forces ▫$R$▫ to be commutative.19902015-07-10 14:46:09Članek v reviji51428UDK: 512.552OceCobissID: 1327364COBISS_ID: 3081220ISSN pri članku: 0001-9054NUK URN: URN:SI:UM:DK:H3L0IM2Gsl