| Title: | Two results concerning symmetric be-derivations on prime rings |
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| Authors: | ID Vukman, Joso (Author) |
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| Files: |  http://dx.doi.org/10.1007/BF02112294
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| Language: | English |
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| Work type: | Article |
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| Typology: | 1.01 - Original Scientific Article |
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| Organization: | PEF - Faculty of Education
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| Abstract: | 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. |
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| Keywords: | matematika, asociativni kolobarji in algebre, kolobar, prakolobar, odvajanje, simetrično bi-odvajanje, mathematics, associative rings and algebras, ring, prime ring, derivation, symmetric bi-derivation |
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| Year of publishing: | 1990 |
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| Number of pages: | str. 181-189 |
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| Numbering: | Vol. 40, iss. 1 |
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| PID: | 20.500.12556/DKUM-51428  |
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| UDC: | 512.552 |
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| ISSN on article: | 0001-9054 |
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| COBISS.SI-ID: | 3081220 |
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| NUK URN: | URN:SI:UM:DK:H3L0IM2G |
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| Publication date in DKUM: | 10.07.2015 |
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| Views: | 1144 |
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| Downloads: | 42 |
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| Metadata: |    |
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| Categories: | Misc.
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