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Journal of Discrete Mathematical Sciences and Cryptography

(Since 1998)
Open Access ·Peer-reviewed·ISSN (Online): 2169-0065·ISSN (Print): 0972-0529

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Journal of Discrete Mathematical Sciences and Cryptography
Open Access Research Article

Several types of derivations on prime and semiprime gamma rings

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pp. 1705–1714Vol. 27Issue 5August 2024DOI: 10.47974/JDMSC-2012 Crossmark XML
Received:
16 Jan 2024
Published Online:
26 Aug 2024
Article type:
Research Article
Language:
EN
Article no.:
JDMSC-2012
Pages:
1705–1714

Abstract

In this paper the notion of asymmetric skew 4-derivation of prime and semiprime Γ-ring is presented and studied. Therefore we proved that; presume Ň be a 3,2-torsion free non commutative prime Γ-rings accomplishing a certain assumption and L be admissible Lie ideal of Ň; Let : Ň4→Ň is a symmetric 4-derivation. If f is a trace of such that [f(s),s]σ = 0; for each one s ∈ L, σ ∈ Γ therefore = 0,also we prove that; if Ň be a 3,2−torsion free non commutative semiprime Γ-rings accomplishing a certain assumption and L be admissible Lie ideal of Ň. Presume a is an automorphism of Ň and : Ň4→Ň is a symmetric skew 4-derivation associated with a. Presume that the trace function f is commuting on L such that [f(s), a(s)]σ ∈ Z for each s ∈ L, σ ∈ Γ, where f(L) ⸦ L, therefore [f(s), a(s)]σ = 0 for eachs ∈ L, σ ∈ Γ,the quantity demand and investment in research and development, while the other model focuses on a more realistic relationship between the quantity demand and the price. 

Keywords

Prime (semiprime) Γ-ringsSkew 4- derivationCommutingCentralizingAdmissible lie ideal

Subject Classifications

Primary 93A30Secondary 49K15

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