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Mathematica Slovaca

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Volume 68, Issue 5

Issues

A note on automorphisms of lie ideals in prime rings

Bijan Davvaz / Mohd Arif Raza
Published Online: 2018-10-20 | DOI: https://doi.org/10.1515/ms-2017-0179

Abstract

In the present paper, we prove that a prime ring R with center Z satisfies s4, the standard identity in four variables if R admits a non-identity automorphism σ such that (uσ,u]vσ+vσ[uσ,u])nZ for all u,v in some non-central Lie ideal L of R whenever either char(R)>n or char(R)=0, where n is a fixed positive integer.

MSC 2010: Primary 16N60, 16W20; Secondary 16R50

Keywords: prime ring; automorphism; maximal right; ring of quotients; generalized polynomial identity (GPI); Lie ideal

  • [1]

    ALI, S.—HUANG, S.: On derivations in semiprime rings, Algebr. Represent. Theo. 15 (2012), 1023–1033.Google Scholar

  • [2]

    BEIDAR, K. I.—MARTINDALE III, W. S.—MIKHALEV, A. V.: Rings with Generalized Identities. Pure Appl. Math. 196, Marcel Dekker, New York, 1996.Google Scholar

  • [3]

    BREŠAR, M.: Centralizing mappings and derivations in prime ring, J. Algebra 156 (1993), 385–394.Google Scholar

  • [4]

    BREŠAR, M.: Commuting traces of biadditive mappings, commutativity preserving mappings and Lie mappings, Trans. Amer Math. Soc. 335(2) (1993), 525–546.Google Scholar

  • [5]

    BREŠAR, M.: On a generalization of the notion of centralizing mappings, Proc. Amer. Math. Soc. 114 (1992), 641–649.Google Scholar

  • [6]

    CARINI, L.—DE FILIPPIS, V.: Commutators with power central values on Lie ideals, Pacific J. Math. 193 (2000), 269–278.Google Scholar

  • [7]

    CHUANG, C. L.: GPIs having coefficients in Utumi quotient rings, Proc. Amer. Math. Soc. 103 (1988), 723–728.Google Scholar

  • [8]

    CHUANG, C. L.: Differential identities with automorphism and anti-automorphism-II, J. Algebra 160 (1993), 291–335.Google Scholar

  • [9]

    CHENG, H.: Some results about derivations of prime rings, J. Math. Reser. Expos. 25(4) (2005), 625–633.Google Scholar

  • [10]

    HERSTEIN, I. N.: Derivations of prime rings having poer central values, Contemp. Math. 13 (1982), 163–171.Google Scholar

  • [11]

    HUANG, S.: Derivations with Engel conditions in prime and semiprime rings, Czechoslovak Math. J. 61(136) (2013), 1135–1140.Google Scholar

  • [12]

    JACOBSON, N.: PI-algebras, An Introduction. Lecture Notes in Math. 441, Berlin Heidelberg, New york: Springer Verlag, 1975.Google Scholar

  • [13]

    LANSKI, C.: Differential identities, Lie ideals and Posner’s theorems, Pacific J. Math. 134 (1988), 275–297.Google Scholar

  • [14]

    LANSKI, C.: An Engel condition with derivations, Proc. Amer. Math. Soc. 118 (1993), 731–734.Google Scholar

  • [15]

    LEE, P. H.—LEE, T. K.: Lie ideals of prime rings with derivations, Bull. Inst. Math. Acad. Sin. 11 (1983), 75–80.Google Scholar

  • [16]

    MARTINDALE III, W. S.: Prime rings satisfying a generalized polynomial identity, J. Algebra 12 (1969), 576–584.Google Scholar

  • [17]

    MAYNE, J. H.: Centralizing automorphisms of prime rings, Canad. Math. Bull. 19 (1976), 113–115.Google Scholar

  • [18]

    MAYNE, J. H.: Centralizing automorphisms of Lie ideals in prime rings, Canad. Math. Bull. 35 (1992), 510–514.Google Scholar

  • [19]

    POSNER, E. C.: Derivations in prime rings, Proc. Amer. Math. Soc. 8 (1957), 1093–1100.Google Scholar

  • [20]

    RAZA, M. A.—REHMAN, N.: An identity on automorphisms of Lie ideals in prime rings, Ann. Univ. Ferrara 62(1) (2016), 143–150.Google Scholar

  • [21]

    REHMAN, N.—RAZA, M. A.: On m-commuting mappings with skew derivations in prime rings, St. Petersburg Math. J. 27(4) (2016), 641–650.Google Scholar

  • [22]

    VUKMAN, V.: Commuting and centralizing mappings in prime rings, Proc. Amer. Math. Soc. 109(1) (1990), 47–52.Google Scholar

  • [23]

    VUKMAN, V.: Identities with derivations and automorphis on semiprime rings, Int. J. Math. Math. Sci. 2005(7) (2005), 1031–1038.Google Scholar

  • [24]

    WANG, Y.: Power-centralizing automorphisma of Lie ideals in prime rings, Comm. Algebra 34 (2006),609–615.Google Scholar

About the article

Received: 2016-05-21

Accepted: 2017-10-18

Published Online: 2018-10-20

Published in Print: 2018-10-25


Communicated by Miroslav Ploščica


Citation Information: Mathematica Slovaca, Volume 68, Issue 5, Pages 1223–1229, ISSN (Online) 1337-2211, ISSN (Print) 0139-9918, DOI: https://doi.org/10.1515/ms-2017-0179.

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