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令K=(RNMS)是一个具有零迹理想的形式矩阵环,σ是K的一个满足σ(E11)=E11,σ(E22)=E22的自同构.本文确定了K的σ-双导子和σ-交换映射的一般形式,证明了在一定条件下K的每个σ-双导子都可以表示成一个外σ-双导子与一个内 σ-双导子的和.此外,本文给出了K的任意σ-双导子(σ-交换映射)是内 σ-双导子(真σ-交换映射)的一个充分条件.“,”Let K=(RNMS)be a formal matrix ring with zero trace ideals and σ an automorphism of K with σ(En)=E11 and σ(E22)=E22.In this paper,we determine the general form of σ-biderivations and σ-commuting mappings of K,and prove that under certain conditions every σ-biderivation of K is a sum of an inner σ-biderivation and an extremalσ-biderivation.Moreover,we give a sufficient condition on K for all of its σ-biderivations(respectively,σ-commuting mappings)to be inner(respectively,proper).