Annihilator on prime rings admitting multiplicative generalized g-derivations

Suppose ℜ is a ring and g:ℜ→Qr be an arbitrary map. An additive map d:ℜ→Qr is said to be g-derivation if d(xy)=d(x)y+g(x)d(y) holds forallx,y∈ℜ. An additive map G:ℜ→Qr is said to be generalized g-derivation if G(xy)=G(x)y+g(x)d(y) holds forallx,y∈ℜ. For any subset S of ℜ, S⊆ℜ. The left annihilator of S in ℜ is denoted by lℜ(S) and defined by lℜ(S)={x∈ℜ∣xS=0}. In the present paper, we study the left annihilator identities on prime rings admitting multiplicative generalized g-derivations. © The Author(s) under exclusive license to Università degli Studi di Ferrara 2024.