Abstract: This paper gives the definition of e-invertible matrices, which is a generalization of invertible matrices over semirings. Through exploring the interrelationships between invertible matrices and e-invertible matrices, the equivalent characterizations of e-invertible matrices over commutative semirings are given. Also, by studying the  semigroup of e-invertible matrices, the decomposition theorem of such matrices semigroup over commutative semirings is obtained. Finally, it proves that such matrices semigroup exists a maximal subgroup, and the union of all maximal subgroups forms a Clifford semigroup.

Key words: e-invertible matrices, maximal subgroup, subdirect product, Clifford semigroup

摘要： 对半环上可逆矩阵的概念进行推广，给出了[e]-可逆矩阵的定义。通过探讨可逆矩阵与[e]-可逆矩阵之间的内在联系，给出了交换半环上[e]-可逆矩阵的等价刻画。同时，对交换半环上[e]-可逆矩阵的全体关于矩阵乘法构成的半群进行研究，给出了此类矩阵半群的分解定理，并证明了此类矩阵半群均存在极大子群，且所有极大子群的并是Clifford半群。

关键词: [e]-可逆矩阵, 极大子群, 次直积, Clifford半群