Some Properties On Regular ～*-Semigroups And One Sided Homomorphisms On Semigroups

This paper is devoted exclusively to the properties on regular *- semigroups and one sided homomorphisms on semigroups. It contians four sections.Section one is introduction.In section 2, a partial order on a regular *- semigroup is described, and some sufficient and necessary conditions for the natural partial order to be compatiable are given. Furthermore, the properties on a unitary set of a regular *- semigroup are discussed.In section 3, a construction of all subdirect products of regular *- semigroups is obtained. As an application, E-unitary covers for regular *- semigroups is investigated. Furthermore, the spined products are discussed. In the end of the section, the semidirect products are discussed.In section 4, a concept of one sided homomorphism is introduced, and some corresponding resules are presented.