Study On The Structure Of Some=~U-Abundant Semigroups

In this paper,we mainly study =^U-abundant semigroups,and some properties and some structure theorems of such semigroups are given.The main idea is to describe structures and properties of generalized regular semigroups by generalized Green relations in generalized regular semigroups.There are three chapters,the main contest are given in follow:In the first chapter,we used Green =^Urelations to define PI-strong???-abundant semigroups,to discuss its fundamental properties and texture of the product.The main results are given in follow:Theorem 1.3.1 Let S be a PI-strong???-abundant semigroup,then S?U×S/?.In the second chapter,we used Green =^U relations to define Quasi strong ?n,m?-=^U-abundant semigroups,strong-?n,m?-=^U-abundant semigroups,to discuss their fundamental properties.The main results are given in follow:Theorem 2.2.6 Let S be a quasi strong???-abundant semigroup and ???? U????E?Sm???,and U is a,subsemigroup of S,then[e?Sme?]is a quasi strong?n,m?-=^U-abundant semigroups.Theorem 2.3.3 Let J is a strong?n,m?-=^U-abundant semigroups,then each???-classes of S and each???-classes of S contain the only idempotent in U,that is for all a ? Sm,Theorem 2.3.4 Let a is a strong?n,m?-=^U abundant semigroups,then?1?for???????S+,????Sm,?2?for???????Sm,????S+.Theorem 2.3.4 Let S is a strong?n,m?-=^U abundant semigroups,U????E?Sm??? and U is subsemigroup of S,then for???a ? Sm,e ? U,In the third chapter:Using the relationship on the???,eventually=^? abundant semigroup are defined,eventually strong Cu abundant semigroup,and give the description of their structure.The main result is given in follow:Theorem 3.27.If S is eventually PI-strong???-abundant semigroup if and only S is strong semilattice of exchange cancellative Ta and a inflation S?=[T?×U?;??]???Y?of direct product on rectangular band U?,U=???Y{1T?}×U? is subsemigroup.