On some functional equations in rings
Abstract
In this article we prove the following result. Let ▫$n \ge 1$▫ be some fixed integer, and let ▫$R$▫ be a prime ring with ▫$2n \le char(R) \ne 2$▫. Suppose there exists an additive mapping ▫$T: R \to R$▫ satisfying the relation ▫$T(x^{2n+1}) = \sum_{i=1}^{2n+1}(-1)^{i+1} x^{i-1} T(x)x^{2n+1-i}$▫ for all ▫$x \in R$▫. In this case, ▫$T$▫ is of the form ▫$4T(x) = qx + xq$▫ for all ▫$x \in R$▫, where ▫$q$▫ is some fixed element from the symmetric Martindale ring of quotients. This result makes it possible to solve some functional equations in prime rings with involution which are related to bicircular projections.
Keywords
funkcijska identiteta;odvajanje;bicirkularna projekcija;jordansko trojno odvajanje;prakolobar;kolobar z involucijo;polprakolobar;bicircular projection;derivation;functional identity;Jordan tripple derivation;prime ring;ring with involution;semiprime ring;
Data
| Language: | English |
|---|---|
| Year of publishing: | 2011 |
| Typology: | 1.01 - Original Scientific Article |
| Organization: | UM FNM - Faculty of Natural Sciences and Mathematics |
| UDC: | 512.552.3 |
| COBISS: |
18550536
|
| ISSN: | 0092-7872 |
| Views: | 1005 |
| Downloads: | 83 |
| Average score: | 0 (0 votes) |
| Metadata: |
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Other data
| Secondary language: | Slovenian |
|---|---|
| Secondary title: | Nekatere funkcijske enačbe na kolobarjih |
| Secondary keywords: | funkcijska identiteta;odvajanje;bicirkularna projekcija;jordansko trojno odvajanje;prakolobar;kolobar z involucijo;polprakolobar; |
| URN: | URN:SI:UM: |
| Pages: | str. 2647-2658 |
| Volume: | ǂVol. ǂ39 |
| Issue: | ǂno ǂ7 |
| Chronology: | 2011 |
| ID: | 8723784 |
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