Taiwanese Journal of Mathematics

COMMUTING MAPS: A SURVEY

Matej Breˇsar

Full-text: Open access

Abstract

A map $f$ on a ring $\cal A$ is said to be commuting if $f(x)$ commutes with $x$ for every $x\in \cal A$. 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.

Article information

Source
Taiwanese J. Math., Volume 8, Number 3 (2004), 361-397.

Dates
First available in Project Euclid: 18 July 2017

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1500407660

Digital Object Identifier
doi:10.11650/twjm/1500407660

Mathematical Reviews number (MathSciNet)
MR2163313

Subjects
Primary: 16R50: Other kinds of identities (generalized polynomial, rational, involution) 16W10: Rings with involution; Lie, Jordan and other nonassociative structures [See also 17B60, 17C50, 46Kxx] 16W25: Derivations, actions of Lie algebras 16N60: Prime and semiprime rings [See also 16D60, 16U10] 46H40: Automatic continuity 47B47: Commutators, derivations, elementary operators, etc.

Keywords
commuting map functional identity prime ring Banach algebra derivation Lie theory linear preservers

Citation

Breˇsar, Matej. COMMUTING MAPS: A SURVEY. Taiwanese J. Math. 8 (2004), no. 3, 361--397. doi:10.11650/twjm/1500407660. https://projecteuclid.org/euclid.twjm/1500407660


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