矩阵逆半群

矩阵逆半群

We discuss some fundamental properties of inverse semigroups of matrices, and prove that the idempotents of such a semigroup constitute a subsemilattice of a finite Boolean lattice,and that the inverse semigroups of some matrices with the same rank are groups. At last, we determine completely the construction of the inverse semigroups of some 2 x 2 matrices: such a semigroup is isomorphic to a linear group of dimension 2 or a null-adjoined group, or is afinite semilattice of Abelian linear groups of finite dimension, or satisfies some other properties.The necessary and sufficient conditions are given that the sets consisting of some 2 × 2 matrices become inverse semigroups.

作 者： 朱用文 ZHU Yong Wen   作者单位： School of Mathematics and Information Science, Yantai University, Shandong 264005, China  刊 名： 数学研究与评论  ISTIC PKU 英文刊名： JOURNAL OF MATHEMATICAL RESEARCH AND EXPOSITION  年，卷(期)： 2008 28(3)  分类号： O152.7  关键词： matrix semigroup   inverse semigroup   Green's relation   Clifford. semigroup   semi-lattice  

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