关键词: [e]-可逆矩阵, 极大子群, 次直积, Clifford半群

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