Special Properties Of Irregular Semigroup

The paper is devoted to the special properties of irregular semigroups,mainly from the subsemigroup latticeto describe the properties of irregular semigroups,especially subsemigroup lattice and full subsemigroup lattice of the GV-inverse semigroups.The paper consists of four chapters:The first chapter is the introduction part,which mainly elaborates the thesis background and current situation and the research ideas of the thesis.The second chapter mainly studies theproperties of subsemigroup lattice of GV-inverse semigroupswhich subsemigrouplattice is $-semidistributive,the introduction of nilsemigroup and epigroups,to describe theproperties of subsemigroup lattice of GV-inverse semigroupswhich subsemigrouplattice is ^-semidistributive,at the same time for some inferences,get the new conclusions,and showed a sufficient and necessary condition for subsemigrouplattice is ^-semidistributive.The third chapter mainly studiesthe properties of subsemigroup lattice of GV-inverse semigroupswhich subsemigrouplattice is 0-modular,the introduction of unipotentepigroup and band to describe theproperties that subsemigrouplattice is 0-modular,when the conditions are given,ES is band,and showed a sufficient and necessary condition for subsemigrouplattice is 0-modular.The fourth chapter mainly studied the properties of full subsemigroup lattice of the GV-inverse semigroups,especially the full subsemigrouplattice is a distributive lattice,the introduction of unipotentepigroup and semigroup homomorphism to describetheproperties that full subsemigrouplattice is distributive,and showed a sufficient and necessary condition for full subsemigrouplattice is distributive.