形式三角矩阵半环的导子与高阶导子

On derivations and higher derivations of a formal triangular matrix semiring

研究了形式三角矩阵半环Tri(R,M,S)的导子和高阶导子.证明了半环Tri(R,M,S)的任一导子可由半环R,S的导子和(R,S)-双半模M的一个拟同态来表示;半环Tri(R,M,S)的任一高阶导子可由半环R,S的高阶导子和(R,S)-双半模M中满足一定条件的一族可加映射来表示.

The derivations and the higher derivations of a formal triangular matrix semiring Tri(R,M,S)are studied in this paper,and it is proved that any derivation of the semiring Tri(R,M,S)can be expressed by a derivation of the semiring R and a derivation of the semiring S and a quasi-homomorphism of the(R,S)-bi-semimodule M,and that any higher derivation of Tri(R,M,S)can be expressed by a higher derivation of Rand a higher derivation of S and a family of additive mappings of the(R,S)-bi-semimodule M which satisfy some conditions.