K. I. Beidar, A. V. Mikhalev, M. A. Chebotar, “Functional identities in rings and their applications”, Russian Math. Surveys, 59:3 (2004), 403

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Russian Mathematical Surveys, 2004, Volume 59, Issue 3, Pages 403–428
DOI: https://doi.org/10.1070/RM2004v059n03ABEH000735 (Mi rm735)

This article is cited in 21 scientific papers (total in 21 papers)

Functional identities in rings and their applications

K. I. Beidar^a, A. V. Mikhalev^b, M. A. Chebotar^c

^a National Cheng Kung University
^b M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
^c Tula State University

English version PDF (388 kB) Citations (21) Russian version article

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DOI: https://doi.org/10.1070/RM2004v059n03ABEH000735

Abstract: In the present survey the main results of the theory of functional identities are presented and an analysis of the current state of this theory is given. Applications obtained in this direction include the solution of all the Herstein problems concerning maps of Lie type, the description of Lie-admissible multiplications, and characterizations of commutativity-preserving maps and of maps preserving normal elements.

Received: 15.09.2003

Bibliographic databases:

Document Type: Article

UDC: 512.552

MSC: Primary 16R50, 17A30; Secondary 16W10, 17D25, 16N60, 17B60, 17C50, 17A05, 17A20

Language: English

Original paper language: Russian

Citation: K. I. Beidar, A. V. Mikhalev, M. A. Chebotar, “Functional identities in rings and their applications”, Russian Math. Surveys, 59:3 (2004), 403–428

Citation in format AMSBIB

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Linking options:

https://www.mathnet.ru/eng/rm735

https://doi.org/10.1070/RM2004v059n03ABEH000735

https://www.mathnet.ru/eng/rm/v59/i3/p3

This publication is cited in the following 21 articles:

Benjamin Marcen, Joso Vukman, “On certain functional equation related to derivations”, Open Mathematics, 22:1 (2024)
Maja Fošner, Benjamin Marcen, Joso Vukman, “On a functional equation characterizing two-sided centralizers in prime rings”, Period Math Hung, 86:2 (2023), 538
Maja Fošner, Benjamin Marcen, “A new equation related to two-sided centralizers in prime rings”, Aequat. Math., 96:6 (2022), 1207
Fosner M., Marcen B., Vukman J., “On Some Functional Equation Arising From (M, N)-Jordan Derivations of Prime Rings”, Publ. Math.-Debr., 92:1-2 (2018), 133–146
Fosner M., Marcen B., Sirovnik N., Vukman J., “On Some Functional Equations Related To Derivations and Bicircular Projections in Rings”, Glas. Mat., 49:2 (2014), 313–331
A. R. Chekhlov, Ml. V. Agafontseva, “Ob abelevykh gruppakh s tsentralnymi kvadratami kommutatorov endomorfizmov”, Vestn. Tomsk. gos. un-ta. Matem. i mekh., 2013, no. 4(24), 54–59
Fosner M., Vukman J., “On Some Functional Equations Arising From (M, N)-Jordan Derivations and Commutativity of Prime Rings”, Rocky Mt. J. Math., 42:4 (2012), 1153–1168
Maja Fosner, Joso Vukman, “Equations related to derivations on prime rings”, Glas. Mat. Ser. III, 46:1 (2011), 31
Maja Fošner, Joso Vukman, “On Some Functional Equations in Rings”, Communications in Algebra, 39:7 (2011), 2647
A. S. Gordienko, “Codimensions of functional identities”, Russian Math. Surveys, 64:1 (2009), 148–149
Wang Yu., “A note on range-inclusive maps in rings with idempotents”, Comm. Algebra, 37:11 (2009), 3827–3832
Wang Yu., “Functional identities and Lie superhomomorphisms on prime superalgebras”, Comm. Algebra, 37:12 (2009), 4193–4226
Fošner M., Vukman J., “An equation related to two-sided centralizers in prime rings”, Houston J. Math., 35:2 (2009), 353–361
Fošner M., Vukman J., “On some equations in prime rings”, Monatsh. Math., 152:2 (2007), 135–150
Vukman J., Fošner M., “A characterization of two-sided centralizers on prime rings”, Taiwanese J. Math., 11:5 (2007), 1431–1441
Chebotar M.A., Ke Wen-Fong, Lee Pjek-Hwee, Zhang Ruibin, “On maps preserving zero Jordan products”, Mh Math, 149:2 (2006), 91–101
Chebotar M.A., Fong Y., “The life contribution of Kostia Beidar in ring and nearring theory”, Taiwanese J. Math., 10:6 (2006), 1409–1417
A. V. Mikhalev, M. A. Chebotar, V. T. Markov, “Konstantin Igorevich Beidar (1951–2004)”, J. Math. Sci., 149:2 (2008), 1039–1046
Chebotar M.A., Fong Yuen, Lee Pjek-Hwee, “On maps preserving zeros of the polynomial $xy-yx$ ”, Linear Algebra Appl., 408 (2005), 230–243
Chebotar M.A., Ke W.-F., Lee P.-H., Shiao L.-S., “On maps preserving products”, Canad. Math. Bull., 48:3 (2005), 355–369

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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Abstract page:	754
Russian version PDF:	320
English version PDF:	38
References:	102
First page:	3

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