Categories * - Semirings

The theory of fixed points and pre-fixed points play a very important role in the theory of semirings.In this paper,we will study some classes*-semirings related to the fixed points and pre-fixed points.The main results are as follows:1. *1-λ-semirings is sdudied,which is a special class of *-λ-semirings.We have got some new resuls,and proved that if S is *1-λ-semirings,then for any non-negative integer n,the set of n-order matrix over S is also a *1'-λ-semirings. If S is*1-λ-semirings,then S is not only a weak inductive*-semirings,but also a Conway semirings.2.We introduce and studyμ-*-semirings andλ-*-semirings.Obviously,*-μ-semirings isμ-*-semirings.But it does not hold on the contrary.We give out a necessary and suffcient condition that aμ-*-semirings is a *-μ-semirings.It is easy to know that a*-λ-semirings isλ-*-semirings.But it does not hold on the contrary.We give out a necessary and suffcient condition that aλ-*-semirings is a *-λ-semirings.3. We study *-λ-semirings,idempotent *-λ-semirings and idempotent *1-λ-semirings. Proved that if a semirings S is an idempotent *-λ-semirings or idempotent *1-λ-semirings,then 1*=1.