Commuting maps: a survey
Abstract
Preslikava ▫$f$▫ na kolobarju ▫$A$▫ je komutirajoča, če ▫$f(x)$▫ komutira z ▫$x$▫ za vsak ▫$x$▫ iz ▫$A$▫. Članek opiše razvoj teorije komutirajočih preslikav in njenih aplikacij. Obravnavane so naslednje teme: komutirajoča odvajanja, komutirajoče aditivne preslikave, komutirajoče sledi mulitiaditivnih preslikav, različne posplošitve pojma komutirajočih preslikav, in aplikacije rezultatov o komutirajočih preslikavah na različnih področjih, predvsem v teoriji Liejevih algeber.
Keywords
matematika;algebra;prakolobar;komutirajoča preslikava;funkcijska identiteta;Banachova algebra;odvajanje;Liejeve algebre;linearni ohranjevalci;ne zaključna dela;mathematics;commuting map;functional identity;prime ring;Banach algebra;derivation;Lie theory;linear preservers;
Data
| Language: | English |
|---|---|
| Year of publishing: | 2004 |
| Typology: | 1.02 - Review Article |
| Organization: | UM PEF - Faculty of Education |
| UDC: | 512.552 |
| COBISS: |
13330265
|
| ISSN: | 1027-5487 |
| Views: | 1372 |
| Downloads: | 27 |
| Average score: | 0 (0 votes) |
| Metadata: |
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Other data
| Secondary language: | Slovenian |
|---|---|
| Secondary title: | Komutirajoče preslikave: pregledni članek |
| Secondary abstract: | A map ▫$f$▫ on a ring ▫$\mathcal{A}$▫ is said to be commuting if ▫$f(x)$▫ commutes with ▫$x$▫ for every ▫$x \in \mathcal{A}$▫. The paper surveys the development of the theory of commuting maps and their applications. The following topics are discussed: commuting derivations, commuting additive maps, commuting traces of multiadditive maps, various generalizations of the notion of a commuting map, and applications of results on commuting maps to different areas, in particular to Lie theory. |
| Secondary keywords: | Algebra; |
| URN: | URN:SI:UM: |
| Type (COBISS): | Article |
| Pages: | str. 361-397 |
| Volume: | ǂVol. ǂ8 |
| Issue: | ǂno. ǂ3 |
| Chronology: | 2004 |
| DOI: | 10.11650/twjm/1500407660 |
| ID: | 1472410 |
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