On generalized (α,β)-derivations and Lie ideals of prime rings

被引:0
|
作者
Sandhu, Gurninder S. [1 ]
Ali, Shakir [2 ]
Boua, Abdelkarim [3 ]
Kumar, Deepak [4 ]
机构
[1] Patel Mem Natl Coll, Dept Math, Rajpura, India
[2] Aligarh Muslim Univ, Fac Sci, Dept Math, Aligarh, Uttar Pradesh, India
[3] Sidi Mohammed Ben Abdellah Univ, Polydisciplinary Fac, LSI, Taza, Morocco
[4] Punjabi Univ, Dept Math, Patiala, Punjab, India
关键词
Prime ring; Generalized derivation; Generalized; (alpha; beta)-derivation; Square-closed Lie ideal; DERIVATIONS; COMMUTATIVITY;
D O I
10.1007/s12215-021-00685-9
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
Let R be a prime ring and alpha, beta be the automorphisms of R. The main aim of this article is to investigates several algebraic identities involving generalized (alpha, beta)-derivations acting on Lie ideals of prime rings. More precisely, we study the following identities: (i) F([x, y]) = alpha(x)circle F(y), (ii) F(x circle y) = [alpha(x), F(y)], (iii) F(xy) +/- yx. Z(R), (iv) F(xy) is an element of Z(R), (v) F(x)alpha (y) - beta(x)G(y) is an element of Z(R), (vi) F(x)y = xF(y), (vii) a(F(x)F(y) +/- alpha(xy)) = 0, (viii) a(F(x)F(y) +/- alpha(yx)) = 0 for all x, y. L (the nonzero square-closed Lie ideal of R), where 0. a. R is a fixed element. Moreover, some examples are given that exhibit the cruciality of the hypotheses taken.
引用
收藏
页码:499 / 513
页数:15
相关论文
共 50 条
  • [31] Prime Rings with Generalized Derivations on Right Ideals
    Demir, C.
    Argac, N.
    ALGEBRA COLLOQUIUM, 2011, 18 : 987 - 998
  • [32] On generalized derivations and Jordan ideals of prime rings
    Sandhu, Gurninder S.
    Davvaz, Bijan
    RENDICONTI DEL CIRCOLO MATEMATICO DI PALERMO, 2021, 70 (01) : 227 - 233
  • [33] On generalized derivations and Jordan ideals of prime rings
    Gurninder S. Sandhu
    Bijan Davvaz
    Rendiconti del Circolo Matematico di Palermo Series 2, 2021, 70 : 227 - 233
  • [34] On ideals and commutativity of prime rings with generalized derivations
    Abu Nawas, M. K.
    Al-Omary, Radwan M.
    EUROPEAN JOURNAL OF PURE AND APPLIED MATHEMATICS, 2018, 11 (01): : 79 - 89
  • [35] ANNIHILATOR CONDITIONS WITH GENERALIZED SKEW DERIVATIONS AND LIE IDEALS OF PRIME RINGS
    De Filippis, Vincenzo
    Rehman, Nadeem Ur
    Scudo, Giovanni
    INTERNATIONAL ELECTRONIC JOURNAL OF ALGEBRA, 2022, 32 : 192 - 216
  • [36] Lie ideals and (alpha, beta)-derivations of *-prime rings
    Rehman, Nadeem ur
    Golbasi, Oznur
    Koc, Emine
    RENDICONTI DEL CIRCOLO MATEMATICO DI PALERMO, 2013, 62 (02) : 245 - 251
  • [37] Derivations with annihilator conditions on Lie ideals in prime rings
    Huang, Shuliang
    JOURNAL OF ALGEBRA AND ITS APPLICATIONS, 2020, 19 (02)
  • [38] A note on generalized Lie derivations of prime rings
    Nihan Baydar Yarbil
    Nurcan Argaç
    Frontiers of Mathematics in China, 2017, 12 : 247 - 260
  • [39] A note on generalized Lie derivations of prime rings
    Yarbil, Nihan Baydar
    Argac, Nurcan
    FRONTIERS OF MATHEMATICS IN CHINA, 2017, 12 (01) : 247 - 260
  • [40] Generalized skew-derivations acting on Lie ideals with central values in prime rings
    Dhara B.
    ANNALI DELL'UNIVERSITA' DI FERRARA, 2020, 66 (1) : 1 - 12