About Intends To Abundant Semigroups And Cancellative Semirings A Number Of Studies

The present dissertation is devoted to the specially quasiabundant semigroups and the Green's relations on cancellative semirings. It contains three chapter:In Chapter 1, we study a kind of semigroup with a medial impotent , In paper [6], Blyth and McFadden described a method for constructing of a class of regular semigroups. Logauathan [5] also obtain a description of regular semigroups with a medial idempotent. [11] give a decription of abundent semigroups with a medial idempotent. we give a decription of quasiabundent semigroups with a medial idempotent, which generalizes the corresponding ruslts obtained in [5] [6] [11]. In 1.1, 1.2 wo give sonic definations , notations and propositions. 1.3, 1.4 is our most important results.In Chapter 2, we study the idempotent-connected quasiabundant semigroups, A.EI-Qallali and J. B. Fountain give us some important propositions for the idempotent-connected abundant semigroups in [1]. In 2.1, we give basic definations. In 2.2, we give the largest congruenceαin (?)~#. In 2.3 , we obtain a good homomorphism on the idempotent-connected quasiabundant semigroups.In Chapter 3, the cancellative semirings are investigated. In 3.1 we give some impotant results. In 3.2, the Green's relations on cancellative semirings are investigated, especially, the (?)-relation. The set G of all regular elements of cancellative semirings is proved to be a multiplicative group, and moreover we can prove that G is a unitary subsemigroup of R.