Suppose F is a field of characteristic not 2. Let M(n)(F) be the algebra of all n X n matrices over F, and let A(2), A(3), A(-1), and A(#) be the semigroups of all additive operator on M(n)(F) that preserve idempotence, preserve tripotence, preserve inverses of matrices, and preserve group inverses of matrices, respectively. The main result in this paper is that the semigroup A(2) is generated by transposition, similarity, the operators X --> X(tau) for fixed arbitrary injective endomorphisms tau on F, and the operators X --> sigma(tr X) for fixed arbitrary additive maps sigma from F to M(n)(F) with sigma(1) = O. As applications, we determine the structures of A(3), A(-1), and A(#) when the characteristic of F is also not 3. [References: 7]
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机译：假设F是特征不是2的场。令M（n）（F）是F上所有n X n矩阵的代数，令A（2），A（3），A（-1）和A （＃）是M（n）（F）上所有保留幂等，保留三重性，保留矩阵逆和保留矩阵逆的加法算符的半群。本文的主要结果是半群A（2）是通过转置，相似性生成的，对于F上的固定任意内射同构tau的算子X-> X（tau），以及算子X-> sigma（tr X）对于固定的任意加性映射s从F到M（n）（F），其中sigma（1）=O。作为应用，我们确定A（3），A（-1）和A（＃）的结构当F的特性也不是3时。[参考：7]
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