关于交换半环上一类矩阵的研究  

Study on a class of matrices over commutative semirings

作　　者：张丽霞 邵勇 ZHANG Lixia;SHAO Yong(School of Mathematics, Northwest University, Xi’an 710127, China)

机构地区：[1]西北大学数学学院,西安710127

出　　处：《计算机工程与应用》2017年第20期56-60,共5页Computer Engineering and Applications

基　　金：国家自然科学基金(No.11571278);陕西省自然科学研究基金(No.2015JQ1020)

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。This paper gives the definition of e-invertible matrices,which is a generalization of invertible matrices oversemirings.Through exploring the interrelationships between invertible matrices and e-invertible matrices,the equivalentcharacterizations of e-invertible matrices over commutative semirings are given.Also,by studying the semigroup of einvertiblematrices,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 Cliffordsemigroup.

关 键 词：e-可逆矩阵 极大子群 次直积 CLIFFORD半群 

分 类 号：O152.7[理学—数学]