2025/08/11 by Gusti Ayu Dwi Yanti, Indah Emilia Wijayanti, Yanti, Gusti Ayu Dwi +1
Mathematics · #13F20 #16S34 #47B47 #Advanced Topics in Algebra #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Rings and Algebras (math.RA) #Rings, Modules, and Algebras
paper · pdf · doi:10.48550/arxiv.2508.07609
openalex publication_date 2025/08/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let R be a ring with identity, M,N right modules over R. An additive mapping δ from R to R is called derivation on ring R if it satisfies the Leibniz condition. If δ is a derivation on R and f:M → N is a module homomorphism over R, then an additive mapping d:M → N is called a (δ,f)-derivation if it satisfies d(xa)=d(x)a+f(x)δ(a) for all x ∈ M and a ∈ R. An additive mapping δ: R → R is called Jordan derivation on ring R if δ(x2)=δ(x)x+xδ(x) for all x ∈ R, which is the generalization of derivation This paper presents generalization of Posner's First Theorem of (δ,f)-derivation on 2-torsion prime modules. It also provides a generalization of some results in case of 2-torsion free prime modules from ring situation. Moreover, we introduce a Jordan (δ,f)-derivation on modules and prove that every Jordan (δ,f)-derivation on modules is a (δ,f)-derivation on modules.