HOMODERIVATIONS ON RINGS: STRUCTURAL PROPERTIES AND CHARACTERIZATIONS
Abstract
Research in ring theory has produced major advances, particularly in the study of derivations. A related notion is that of a homoderivation, which combines aspects of derivations and ring homomorphisms. An additive map is called a homoderivation if , for every This study provides a comprehensive analysis of the fundamental structural properties of homoderivation mappings. The main results show that the class of homoderivations is closed under direct sums on component rings. In addition, the sum of two homoderations is again a homoderivation, provided the maps are orthogonal. However, scalar multiplication of a homoderivation generally does not yield another homoderivation, highlighting a key structural distinction from classical derivations.
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