On * – k - semirings
نویسندگان
چکیده
A *–k-semiring is an ordered semiring S equipped with a star operation such that for any a,b 2 S, a*b is the least fixed point of the linear mapping x # ax + b over S. The notion of *–k-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 *–k-semirings and obtain results on *–k-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. 2007 Elsevier Inc. All rights reserved.
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