| Title: | An identity with derivations on rings and Banach algebras |
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| Authors: | ID Fošner, Ajda (Author)
ID Fošner, Maja (Author)
ID Vukman, Joso (Author) |
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| Files: |  Demonstratio_mathematica_2008_Fosner,_Fosner,_Vukman_An_identity_with_derivations_on_rings_and_Banach_algebras.pdf (102,89 KB)
MD5: 0D5D0C68988BE04CF63AA98D7FA4157E
 https://www.degruyterbrill.com/journal/key/dema/html?srsltid=AfmBOoriq-oBc5X5wwJLHrccN0WsKDBHgK7zcNZjApFhdHczJA_txV-8
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| Language: | English |
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| Work type: | Scientific work |
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| Typology: | 1.01 - Original Scientific Article |
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| Organization: | FNM - Faculty of Natural Sciences and Mathematics
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| Abstract: | The main purpose of this paper is to study the following: Let m, n, and $k_{i}, i = 1, 2, ..., n$ be positive integers and let $R$ be a $2m(m+ k_{1} + k_{2} + ... + k_{n} -1)!$-torsion free semiprime ring. Suppose that there exist derivations $D_{i} : R \to R, i = 1, 2, ..., n + 1$ , such that $D_{1}(x^{m})x^{k_{1}+...+k_{n}}+x^{k_{1}} D_{2}(x^{m})x^{k_{2}+...+k_{n}}+...+x^{k_{1}+...+k_{n}}D_{n+1}(x^{m})=0$ holds for all $x \in R$. Then we prove that $D_{1}+D_{2}+...+D_{n+1}=0$ and that the derivation $k_{1}D_{2}+(k_{1}+k_{2})D_{3}+...+(k_{1}+k_{2}+...+k{n})D_{n+1}$ maps $R$ into its center. We also obtain a range inclusion result of continuous derivations on Banach algebras. |
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| Keywords: | mathematics, algebra, associative rings and algebras, prime rings, Banach algebras, identities, derivations |
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| Publication status: | Published |
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| Publication version: | Version of Record |
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| Article acceptance date: | 02.09.2007 |
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| Publisher: | De Gruyter Brill |
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| Year of publishing: | 2008 |
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| Number of pages: | Str. 525-530 |
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| Numbering: | Letn. 41, št. 3 |
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| PID: | 20.500.12556/DKUM-65327  |
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| ISSN: | 0420-1213 |
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| UDC: | 512.552 |
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| ISSN on article: | 0420-1213 |
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| COBISS.SI-ID: | 16160776 |
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| NUK URN: | URN:SI:UM:DK:TKMT87FU |
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| Publication date in DKUM: | 31.03.2017 |
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| Views: | 1565 |
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| Downloads: | 509 |
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| Metadata: |    |
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| Categories: | Misc.
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