Year: 2026
Type: article
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.
Institutions: Diponegoro University, Universitas Gadjah Mada
Language: English
Topic: Advanced Topics in Algebra
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
Funder: Universitas Diponegoro
OpenAlex ID: W7204257508