Let $Cal S$ be any semiring and ${Cal M}(Cal S )$ be the set of all $mimes n$ matrices over $Cal S$. If linear operator $T$ is a term rank preserver, then $T$ is a very useful operator for characterization of various preservers on ${Cal M(S)}$. The linear operator $T$ is called a domination preserving operator if $T(A)le T(B)$ for $Ale B$. In this paper, we proved that $T$ is nonsigular domination preserver and $T(A^t)=T(A)^t$ for $Ain {Cal M}_{2,2}(Cal S )$ if and only if $T$ is a term rank preserver on ${Cal M(S)}$.
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机译：假设$ Cal S $是任何半环，而$ { Cal M}（ Cal S）$是$ Cal S $上所有$ m 乘以n $个矩阵的集合。如果线性运算符$ T $是术语等级保留者，则$ T $是表征$ { Cal M（S）} $上各种保留者的非常有用的运算符。如果$ T（A） le T（B）$为$ A le B $，则线性算子$ T $称为控制保持算子。在本文中，我们证明了$ T $是非奇异的控制权保持者，并且在{ Cal M} _ {2,2}（ Cal S中，$ A 的$ T（A ^ t）= T（A）^ t $ ）$，且仅当$ T $是$ { Cal M（S）} $上的术语排名保留者时。
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