HOMODERIVATIONS ON LIE RINGS

Suffi Nuralesa (Department of Mathematics, Faculty of Science and Mathematics, Universitas Diponegoro, Indonesia)
Galang Riki Ramadhan (Department of Mathematics, Faculty of Science and Mathematics, Universitas Diponegoro, Indonesia)
Carolus Pasha Lazuardi Jituprasojo Hatmakelana (Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Gadjah Mada, Indonesia)
Nurul Fadhilah (Department of Mathematics, Faculty of Science and Mathematics, Universitas Diponegoro, Indonesia)
Benediktus Panji Pradipta (Department of Mathematics, Faculty of Science and Mathematics, Universitas Diponegoro, Indonesia)
Nikken Prima Puspita (Department of Mathematics, Faculty of Science and Mathematics, Universitas Diponegoro, Indonesia)

BAREKENG: Jurnal Ilmu Matematika dan Terapan
Vol 20 No 4 (2026): BAREKENG: Journal of Mathematics and Its Application

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.