2023/02/28 by Sk Aziz, Aziz, Sk, Om Prakash +2
Mathematics · #16W10 #16W25 #16W55 #17C27 #Advanced Topics in Algebra #FOS: Mathematics #Finite Group Theory Research #Rings and Algebras (math.RA) #Rings, Modules, and Algebras
paper · pdf · doi:10.48550/arxiv.2302.14571
openalex publication_date 2023/02/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we mainly prove some results on the additivity of maps over rings under certain conditions. First, we discuss a special case of MARTINDALE III's theorem of \cite1969M as a bijective map φ over a ring R with a non-trivial idempotent satisfying φ(ab)=φ(a)φ(b) for all a, b∈ R, is additive. Then we prove that a map D on R satisfying D(ab)=D(a)b+φ(a) D(b) for all a,b∈ R, where φ is the map mentioned above, is additive. Finally, we establish that if a map g over R satisfies g(ab)=g(a)b+φ(a)D(b), for all a,b∈ R and the maps φ and D are mentioned above, then g is additive.