HOMODERIVATIONS ON LIE RINGS

  • Suffi Nuralesa Department of Mathematics, Faculty of Science and Mathematics, Universitas Diponegoro, Indonesia https://orcid.org/0009-0009-8539-4152
  • Galang Riki Ramadhan Department of Mathematics, Faculty of Science and Mathematics, Universitas Diponegoro, Indonesia https://orcid.org/0009-0003-3928-2949
  • Carolus Pasha Lazuardi Jituprasojo Hatmakelana Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Gadjah Mada, Indonesia https://orcid.org/0009-0009-8334-619X
  • Nurul Fadhilah Department of Mathematics, Faculty of Science and Mathematics, Universitas Diponegoro, Indonesia https://orcid.org/0009-0007-4517-8805
  • Benediktus Panji Pradipta Department of Mathematics, Faculty of Science and Mathematics, Universitas Diponegoro, Indonesia https://orcid.org/0009-0000-7413-726X
  • Nikken Prima Puspita Department of Mathematics, Faculty of Science and Mathematics, Universitas Diponegoro, Indonesia https://orcid.org/0000-0002-0127-2628
DOI: https://doi.org/10.30598/barekengvol20iss4pp3109-3122
Keywords: Binary Operations, Homoderivations, Lie Rings

Abstract

Let  be a set equipped with two binary operations, addition  and multiplication . The triple  is a Lie ring if its multiplication is the Lie bracket commutator defined by  for every . A homoderivation on a Lie ring is a mapping  that satisying the equation , for all . The set of all homoderivations on  is denoted by . This paper investigates the structure of  with the binary operations of addition and composition. It is shown that  does not form a ring. Therefore, we introduce a subset  satisfying the  property. Under this condition, it is shown that  forms a ring. Furthermore, using the bracket operator, the structure  is also a Lie ring. In addition, this paper formulates an iteration of homoderivations in terms of the sigma sum of Lie ring elements.

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Published
2026-08-24
How to Cite
[1]
S. Nuralesa, G. R. Ramadhan, C. P. L. J. Hatmakelana, N. Fadhilah, B. P. Pradipta, and N. P. Puspita, “HOMODERIVATIONS ON LIE RINGS”, BAREKENG: J. Math. & App., vol. 20, no. 4, pp. 3109-3122, Aug. 2026.
Issue
Vol 20 No 4 (2026): BAREKENG: Journal of Mathematics and Its Application
Section
Articles

Copyright (c) 2026 Suffi Nuralesa, Galang Riki Ramadhan, Carolus Pasha Lazuardi Jituprasojo Hatmakelana, Nurul Fadhilah, Benediktus Panji Pradipta, Nikken Prima Puspita

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