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This analysis uncovers properties of derivations in non-commutative prime rings, highlighting their subring characteristics.
This paper identifies all derivations associated with two well-known non-commutative prime rings and provides some remarks on one of these derivations, called the prime derivation. Also, it presents two results for some classes of non-commutative prime rings, regarding when the images of derivations on these rings are subrings of them. The paper also includes some illustrative examples and concludes with a set of questions for further exploration of this topic.
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Khalid H. Al-Shaalan (2025) studied this question.
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