In this paper we study the closed subsemigroups of a Clifford semigroup. shown that{∪- αεY＇ Gα, [ Y＇ ε P（Y）} is the set of all closed subsemigroups of It is a Clifford semigroup S = {Y; Gα; Фα,β}, wher...In this paper we study the closed subsemigroups of a Clifford semigroup. shown that{∪- αεY＇ Gα, [ Y＇ ε P（Y）} is the set of all closed subsemigroups of It is a Clifford semigroup S = {Y; Gα; Фα,β}, where Y＇- denotes the suhsemilattice of Y generated by Y＇. In particular, G is the only dosed subsemigroup of itself for a group G and each one of subsemilattiees of a semilattiee is closed. Also, it is shown that the semiring P（S） is isomorphic to the semiring P（Y） for a Clifford semigroup S = [Y; Gα; Фα,β].展开更多
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 ...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 × 2 matrices： such a semigroup is isomorphic to a linear group of dimension 2 or a null-adjoined group, or is a finite 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.展开更多
文摘In this paper we study the closed subsemigroups of a Clifford semigroup. shown that{∪- αεY＇ Gα, [ Y＇ ε P（Y）} is the set of all closed subsemigroups of It is a Clifford semigroup S = {Y; Gα; Фα,β}, where Y＇- denotes the suhsemilattice of Y generated by Y＇. In particular, G is the only dosed subsemigroup of itself for a group G and each one of subsemilattiees of a semilattiee is closed. Also, it is shown that the semiring P（S） is isomorphic to the semiring P（Y） for a Clifford semigroup S = [Y; Gα; Фα,β].
基金the National Natural Science Foundation of China （No. 10571005）.Acknowledgements The author would like to express his gratitude to Professor Guo Yuqi for his encouragement and guidance, also to all referees for their comments.
文摘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 × 2 matrices： such a semigroup is isomorphic to a linear group of dimension 2 or a null-adjoined group, or is a finite 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.
