Study of multiplicative derivation and its additivity

Authors

  • Wasim Ahmed Aligarh Muslim University.
  • Muzibur Rahman Mozumder Aligarh Muslim University.
  • Arshad Madni Aligarh Muslim University.

DOI:

https://doi.org/10.22199/issn.0717-6279-5578

Keywords:

associative ring, derivation, Peirce decomposition

Abstract

In this paper, we modify the result of M. N. Daif [1] on multiplicative derivations in rings. He showed that the multiplicative derivation is additive by imposing certain conditions on the ring ℜ. Here, we have proved the above result with lesser conditions than M. N. Daif for getting multiplicative derivation to be additive.

Author Biographies

Wasim Ahmed, Aligarh Muslim University.

Department of Mathematics.

Muzibur Rahman Mozumder, Aligarh Muslim University.

Dr. Muzibur Rahman Mozumder is a associate professor of department of Mathematics in Aligarh Muslim University.

Arshad Madni, Aligarh Muslim University.

Department of Mathematics.

References

M. N. Daif, “When is a multiplicative derivation additive?”, International Journal of Mathematics and Mathematical Sciences, vol. 14, no. 3, pp. 615-618, 1991. https://doi.org/10.1155/S0161171291000844

M. N. Daif and M. S. Tammam-El-Sayiad, Multiplicative generalized derivations which are additive”, East-West Journal of Mathematics, vol. 9, no. 1, pp. 31-37, 1997.

N. Jacobson, Structure of rings. American Mathematical Society Colloquium Publications, vol. 37, 1964.

W. S. Martindale, “When are multiplicative mappings additive ?, Proceedings of the American Mathematical Society, vol. 21, no. 3, pp. 695-698, 1969. https://doi.org/10.1090/S0002-9939-1969-0240129-7

E.C. Posner, “Derivations in prime rings”, Proceedings of the American Mathematical Society, vol. 8, no. 6, pp. 1093-1100, 1957. https://doi.org/10.2307/2032686

Y. Wang, “The additivity of multiplicative maps on rings”, Communications in Algebra, vol. 37, no. 6, pp. 2351-2356, 2009. https://doi.org/10.1080/00927870802623369

Published

2023-01-26

How to Cite

[1]
Wasim Ahmed, M. Rahman Mozumder, and A. Madni, “Study of multiplicative derivation and its additivity”, Proyecciones (Antofagasta, On line), vol. 42, no. 1, pp. 219-232, Jan. 2023.

Issue

Vol. 42 No. 1 (2023)

Section

Artículos

Copyright (c) 2023 Wasim Ahmed, Dr. Muzibur Rahman Mozumder, Arshad Madni

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