On Prime Ideals in Rings Satisfying Certain Functional Identities
In this note, we will examine the relationship between a generalized derivation <i>ϝ</i> associated with a derivation <i>∂</i> that satisfies specific algebraic identities and the behavior of a factor ring <inline-formula><math xmlns="http://www.w3.org/1998/Math...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2025-03-01
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| Series: | Axioms |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2075-1680/14/4/247 |
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| Summary: | In this note, we will examine the relationship between a generalized derivation <i>ϝ</i> associated with a derivation <i>∂</i> that satisfies specific algebraic identities and the behavior of a factor ring <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>S</mi><mo>/</mo><mi>P</mi></mrow></semantics></math></inline-formula>, where <i>P</i> is a prime ideal of any ring <i>S</i>. We will also explore several consequences and special cases as applications of our findings. Additionally, various examples have been provided to highlight the necessity of the primeness hypothesis in our theorems. |
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| ISSN: | 2075-1680 |