Let R be a commutative ring with identity, Nn(R) the matrix algebra consisting of all n × n strictly upper triangular matrices over R with the usual product operation. An R-linear map φ : Nn(R) → Nn(R) is said ...Let R be a commutative ring with identity, Nn(R) the matrix algebra consisting of all n × n strictly upper triangular matrices over R with the usual product operation. An R-linear map φ : Nn(R) → Nn(R) is said to be an SZ-derivation of Nn(R) if x2 = 0 implies that φ(x)x+xφ(x) = 0. It is said to be an S-derivation of Nn(R) if φ(x2) = φ(x)x+xφ(x) for any x ∈ Nn(R). It is said to be a PZ-derivation of Nn(R) if xy = 0 implies that φ(x)y+xφ(y) = 0. In this paper, by constructing several types of standard SZ-derivations of Nn(R), we first characterize all SZ-derivations of Nn(R). Then, as its application, we determine all S-derivations and PZ- derivations of Nn(R), respectively.展开更多
基金Fond of China University of Mining and Technology
文摘Let R be a commutative ring with identity, Nn(R) the matrix algebra consisting of all n × n strictly upper triangular matrices over R with the usual product operation. An R-linear map φ : Nn(R) → Nn(R) is said to be an SZ-derivation of Nn(R) if x2 = 0 implies that φ(x)x+xφ(x) = 0. It is said to be an S-derivation of Nn(R) if φ(x2) = φ(x)x+xφ(x) for any x ∈ Nn(R). It is said to be a PZ-derivation of Nn(R) if xy = 0 implies that φ(x)y+xφ(y) = 0. In this paper, by constructing several types of standard SZ-derivations of Nn(R), we first characterize all SZ-derivations of Nn(R). Then, as its application, we determine all S-derivations and PZ- derivations of Nn(R), respectively.
