On ??-semirings
A ??-semiring is an ordered semiring S equipped with a star operation such that for any a,b?S, a?b is the least fixed point of the linear mapping x?ax+b over S. The notion of ??-semirings is a generalization of several important concepts such as continuous semirings, (weak) inductive ?-semirings and the Kleene algebras of Conway and Kozen. We investigate several basic properties of ??-semirings and obtain results on ??-semirings in relation to preorders, duality and formal power series. Some of these results can be seen as generalizations of relevant results on inductive ?-semirings.
??-semiring semiring preorder formal power series