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Generalized (σ , τ) higher derivations in prime rings
1Department of Mathematics, Aligarh Muslim University, Aligarh, 202002 India.
Springerplus
|April 12, 2013
Summary
This study investigates generalized Jordan (σ,τ)-higher derivations in rings. It identifies conditions that make these derivations equivalent to generalized (σ,τ)-higher derivations, advancing abstract algebra research.
Area of Science:
- Abstract Algebra
- Ring Theory
- Mathematical Analysis
Background:
- Introduces (σ,τ)-higher derivations and generalized versions within Lie ideals of rings.
- Defines generalized Jordan (σ,τ)-higher derivations and their relationship to generalized (σ,τ)-higher derivations.
Purpose of the Study:
- To determine the specific conditions under which a generalized Jordan (σ,τ)-higher derivation is also a generalized (σ,τ)-higher derivation.
- To explore the theoretical underpinnings of derivation mappings in abstract algebraic structures.
Main Methods:
- Utilizes algebraic manipulation and proof techniques within the framework of ring theory.
- Examines the properties of additive mappings and endomorphisms on Lie ideals.
Main Results:
- Establishes that every generalized (σ,τ)-higher derivation is a generalized Jordan (σ,τ)-higher derivation.
- Provides necessary and sufficient conditions for the converse to hold.
Conclusions:
- The paper clarifies the distinction and overlap between generalized Jordan (σ,τ)-higher derivations and generalized (σ,τ)-higher derivations.
- Offers new insights into the structure and behavior of higher derivations in ring theory.
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