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Azzahra, Dania
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Computer Science & IT Mathematics

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(α, β)-Derivation on Matrix Ring Mn(R) Azzahra, Dania; Fitriani, Fitriani; Faisol, Ahmad
Euler : Jurnal Ilmiah Matematika, Sains dan Teknologi Volume 14 Issue 1 April 2026
Publisher : Universitas Negeri Gorontalo

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.37905/euler.v14i1.37789

Abstract

In ring theory, a derivation is an additive mapping d:R→R satisfying Leibniz’s rule. A well-known generalization of this notion is the (α,β)-derivation, defined with respect to two ring endomorphisms α and β. In this paper, we study (α,β)-derivations on the matrix ring Mₙ(R) and several of its subrings, including scalar matrices, diagonal matrices, and upper and lower triangular matrix rings. It is shown that an (α,β)-derivation on the base ring RRR induces an (α′,β′)-derivation on these matrix subrings via entrywise extension, preserving their structural properties. Furthermore, we examine certain properties of (α,β)-derivations on the direct product ring R×R. In particular, we show that the sum of two (α,β)-derivations does not necessarily form an (α,β)-derivation, which is demonstrated through a counterexample.
Co-Authors AHMAD FAISOL Fitriani Fitriani