Let Nn(R)be the algebra consisting of all strictly upper triangular n × n matrices over a commutative ring R with the identity.An R-bilinear map φ :Nn(R)×Nn(R)→ Nn(R)is called a biderivation if it...Let Nn(R)be the algebra consisting of all strictly upper triangular n × n matrices over a commutative ring R with the identity.An R-bilinear map φ :Nn(R)×Nn(R)→ Nn(R)is called a biderivation if it is a derivation with respect to both arguments.In this paper,we define the notions of central biderivation and extremal biderivation of Nn(R),and prove that any biderivation of Nn(R)can be decomposed as a sum of an inner biderivation,central biderivation and extremal biderivation for n ≥ 5.展开更多
基金Supported by the National Natural Science Foundation of China(GrantNo.10971117)
文摘Let Nn(R)be the algebra consisting of all strictly upper triangular n × n matrices over a commutative ring R with the identity.An R-bilinear map φ :Nn(R)×Nn(R)→ Nn(R)is called a biderivation if it is a derivation with respect to both arguments.In this paper,we define the notions of central biderivation and extremal biderivation of Nn(R),and prove that any biderivation of Nn(R)can be decomposed as a sum of an inner biderivation,central biderivation and extremal biderivation for n ≥ 5.