Exploring Commutativity via Generalized (α, β)-Derivations Involving Prime Ideals

The purpose of this article is to enhance the previous studies regarding the behavior of a quotient ring ℑ/℘, where ℘ is a prime ideal in a ring ℑ. In particular, we are going to explore more general scenarios whenever a ring ℑ admits a generalized (α,β)-derivation associated with an (α,β)-derivatio...

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Bibliographic Details
Published in:Mathematics (Basel) 2024-08, Vol.12 (15), p.2325
Main Authors: Alsowait, Nawaf, Al-omary, Radwan M., Al-Amery, Zakia, Al-Shomrani, Mohammed
Format: Article
Language:English
Subjects:
(α,β)-derivation
Analysis
Automorphisms
Commutative law (Mathematics)
Commutativity
Derivation
generalized (α,β)-derivations
integral domain
Numbers, Prime
prime ideal
quotient ring
Rings (mathematics)
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Summary:The purpose of this article is to enhance the previous studies regarding the behavior of a quotient ring ℑ/℘, where ℘ is a prime ideal in a ring ℑ. In particular, we are going to explore more general scenarios whenever a ring ℑ admits a generalized (α,β)-derivation associated with an (α,β)-derivation ∂ that satisfies certain criteria involving ℘, where α and β are automorphisms on ℑ. Moreover, we provide some examples to demonstrate the importance of the assumptions made in our results.
ISSN:2227-7390
2227-7390
DOI:10.3390/math12152325