About Several Types Of The Omega - ~ * - Half Ring

The algebraic theory of Conway semiring is one of the important projects of theoretical computer science and algebra. The class of ω-Conway semiring and its two subclasses (the class of w-inductive*-semiring, the class of ω-weak inductive*-semiring) are introduced and studied in this dissertation. Some prop-erties of these classes of semirings are given. Ascending, the matrix semirings and the formal power series semirings over these three semirings are researched. The results are as follows:1. It is proved that the matrix semiring Sn×n of order n over ω-Conway semiring S is also ω-Conway semiring.2. It is proved that the matrix semiring Sn×n of order n and the formal power series semiring S<<A*>> over ω-inductive*-semiring S are ω-inductive*-semiring.3. It is proved that the formal power series semiring S<<A*>> over ω-weak inductive*-semiring S is still ω-weak inductive*-semiring if and only if sum-omega equation, i.e.,((?)s,t∈S<<A*>>)(s+t)ω=(s*t)ω+(s*t)*sω holds in S<<A*>>.