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IJMSI 2024, 19(1): 35-49 |
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Baydar Yarbil N, Argaç N. Annihilators of Power Central Values of Generalized Skew Derivations on Lie Ideals. IJMSI 2024; 19 (1) :35-49
URL: http://ijmsi.ir/article-1-1700-en.html
URL: http://ijmsi.ir/article-1-1700-en.html
Abstract:
Let R be a prime ring with center Z(R) and G be a generalized α-derivation of R for α∈ Aut(R). Let a ∈ R be a nonzero element and n be a fixed positive integer.
(i) If aG(x)n ∈ Z(R) for all x ∈ R then aG(x) = 0 for all x ∈ R unless dimCRC = 4.
(ii) If aG(x)n ∈ Z(R) for all x ∈ L, where L is a noncommutative Lie ideal of R then aG(x) = 0 for all x ∈ R unless dimCRC = 4.
(i) If aG(x)n ∈ Z(R) for all x ∈ R then aG(x) = 0 for all x ∈ R unless dimCRC = 4.
(ii) If aG(x)n ∈ Z(R) for all x ∈ L, where L is a noncommutative Lie ideal of R then aG(x) = 0 for all x ∈ R unless dimCRC = 4.
Keywords: Prime ring, Lie ideal, Generalized skew derivation, Generalized derivation, Automorphism, Right Martindale quotient ring, Two-sided Martindale quotient ring, Generalized polynomial identity
Type of Study: Research paper |
Subject:
General
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