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

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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 \({{\cal M}_n}\left(C \right)\) and ℍℝ, for g ≠ h. Examples are given which show that every Jordan left {g, h}-derivation over \({{\cal T}_n}\left(C \right)\), \({{\cal M}_n}\left(C \right)\) and ℍℝ are not left {g, h}-derivations. Also, the Jordan left {g, h}-derivations over \({{\cal T}_n}\left(C \right)\), \({{\cal M}_n}\left(C \right)\) 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.

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Acknowledgement

The authors are thankful to DST, Govt. of India for financial support and Indian Institute of Technology Patna for providing the research facilities. The authors would like to thank the anonymous referee(s) for their careful reading and valuable comments which helped to improve the presentation of the manuscript.

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  1. Department of Mathematics, Indian Institute of Technology Patna, Patna, Bihar, 801 106, India

    Arindam Ghosh & Om Prakash

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  1. Arindam Ghosh
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  2. Om Prakash
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Correspondence to Arindam Ghosh or Om Prakash.

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Ghosh, A., Prakash, O. Jordan Left {g, h}-Derivation over Some Algebras. Indian J Pure Appl Math 51, 1433–1450 (2020). https://doi.org/10.1007/s13226-020-0475-8

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  • DOI: https://doi.org/10.1007/s13226-020-0475-8

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