Jordan Left {g, h}-Derivation over Some Algebras

Arindam Ghosh () and Om Prakash ()
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Arindam Ghosh: Indian Institute of Technology Patna
Om Prakash: Indian Institute of Technology Patna

Indian Journal of Pure and Applied Mathematics, 2020, vol. 51, issue 4, 1433-1450

Abstract: Abstract In this article, left {g, h}-derivation and Jordan left {g, h}-derivation on algebras are introduced. It is shown that there is no Jordan left {g, h}-derivation over $${{\cal M}_n}\left(C \right)$$ ℳ n ( C ) and ℍℝ, for g ≠ h. Examples are given which show that every Jordan left {g, h}-derivation over $${{\cal T}_n}\left(C \right)$$ T n ( C ) , $${{\cal M}_n}\left(C \right)$$ ℳ n ( C ) and ℍℝ are not left {g, h}-derivations. Also, the Jordan left {g, h}-derivations over $${{\cal T}_n}\left(C \right)$$ T n ( C ) , $${{\cal M}_n}\left(C \right)$$ ℳ n ( C ) and ℍℝ are right centralizers, where C is a 2-torsionfree commutative ring. Moreover, we prove the result of Jordan left {g, h}-derivation to be a left {g, h}-derivation over tensor products of algebras as well as for algebra of polynomials.

Keywords: Derivation; Jordan derivation; left {g; h}-derivation; Jordan left {g; h}-derivation; Tensor product of algebras; 16W10; 16W25; 47L35; 11R52 (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/s13226-020-0475-8

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