20.500.12556/DKUM-51428 Two results concerning symmetric be-derivations on prime rings Dva rezultata o simetričnem odvajanju na prakolobarjih Let ▫$R$▫ 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. Naj bo ▫$R$▫ kolobar. Biaditivna simetrična preslikava ▫$D(.,.): R times R to R$▫ je simetrična biderivacija, če je za vsak ▫$y in R$▫ preslikave ▫$x mapsto D(x,y)$▫ derivacija. V članku sta dokazana dva rezultata o simetričnih biderivacijah na prakolobarjih. Prvi rezultat pravi naslednje: če sta ▫$D_1$▫ in ▫$D_2$▫ simetrični biderivaciji na prakolobarju s karakteristiko različno od dva in tri tako, da je ▫$D_1(x,x)D_2(x,x) = 0, quad x in R$▫, potem je ▫$D_1 = 0$▫ ali ▫$D_2 = 0$▫. matematika asociativni kolobarji in algebre kolobar prakolobar odvajanje simetrično bi-odvajanje mathematics associative rings and algebras ring prime ring derivation symmetric bi-derivation true true false Angleški jezik Slovenski jezik Članek v reviji 2015-07-10 14:46:09 2015-07-10 14:46:09 2024-02-27 14:23:21 2019-07-11 07:18:43 1990 0 0 str. 181-189 iss. 1 Vol. 40 1990 0000-00-00 NiDoloceno NiDoloceno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 512.552 1327364 3081220 0001-9054 URN:SI:UM:DK:H3L0IM2G http://dx.doi.org/10.1007/BF02112294 1 https://dk.um.si/Dokument.php?lang=slv&id=75988 Pedagoška fakulteta 0 0 0