A Number Of Studies On The ¦Ð-regular Semigroup

In this paper, we mainly discuss five classes of π- regular semigroups. The paper is divided into five sections.The first section is introduction.The second section is devoted to the investigation of congruences on a right π- inverse semigroup. Three equivalent forms of the minimum group congruence and the minimum π- group congruence on a right π- inverse semigroup are given.In the third section, band congruence and its extension on π-orthodox semigroups are investigated.The fourth section is devoted to semidirect products and wreath products of left (right) π- regular semigroups. The results known for semidirect products and wreath products base on the fact that semigroups have identity elements. We describe the properties of semidirect products and wreath products of two left (right) π-regular semigroups.In the fifth section, the natural order relations on strongly π-inverse semidirect products are discussed. We generalize results for inverse semidirect products.