数学研究与评论
數學研究與評論
수학연구여평론
JOURNAL OF MATHEMATICAL RESEARCH AND EXPOSITION
2008年
3期
549-557
,共9页
matrix semigroup%inverse semigroup%Green's relation%Clifford. semigroup%semi-lattice
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.
