Star Construction Of Semirings Ⅱ

In this paper, based on [6], we introduce the concepts of star simple (star) scmirings, star congruence free scmirings, congruence free star semirings, entire star semirings and divisible star semirings. And we discuss the star construction of semirings.The paper is separated into four parts. Firstly, we give some basic definitions and examples. Secondly, we study star simple semirings and star congruence free semirings, and discuss the relation of star simple semirings and hemirings in [2]. Thirdly, we study star simple star semirings and congruence free star semirings, and lead to the characterization of divisible star semirings and star semifield. lastly, we define the retract star extension of semirings.