Categories * - Half Ring And Its Initial Semi-ring

This dissertation studies several *-semirings and the initial semirings of them.The main results are as follows:1.The partial *-λ-semirings are introduced and studied.Some qualities of the partial *-λ-semirings are gotten.It is proved that for each n≥0,all n×n upper(lower)triangular matrix semirings in partial *-λ-semirings are partial *-λ-semirings；the semirings of formal power series with coefficients in partial *-λ-semirings also are partial *-λ-semirings.2. The properties of 1 *on Conway semirings on the base of the previous theory are studied. Meanwhile,a congruence on initial Conway semirings is constructed.Guotient semirings about this congruence on initial Conway semir-ings are given.It is proofed that the quotient semirings are ismorphic to initial iteration semirings.3. The qualities of 1* on *-λ-semirings,weak inductive *-semirings and locally closed *-semirings are given.The initial locally closed *-semirings are given by constructed a congruence on initial iteration semirings.