nLab Conway semiring

Definition

A Conway semiring or Conway rig is a quasiregular rig $(R, 0, 1, +, (-)(-), (-)^*)$ such that

• for all $x \in R$ and $y \in R$, $(x + y)^* = (x^* y)^* x^*$

• for all $x \in R$ and $y \in R$, $(x y)^* = 1 + x (y x)^* y$

Related concepts

• rig, semiring

• quasiregular rig

• iteration semiring?

References

• Wikipedia, Conway semiring

• Manfred Droste, Werner Kuich, Semirings and Formal Power Series (2009). In: Manfred Droste, Werner Kuich, Heiko Vogler (editors), Handbook of Weighted Automata. Monographs in Theoretical Computer Science. An EATCS Series. Springer, Berlin, Heidelberg. pp. 3–28.(doi:10.1007/978-3-642-01492-5_1)

• Zoltán Ésik, Iteration semirings (2008). In: Masami Ito, Masafumi Toyama (editors), Developments in language theory. 12th international conference, DLT 2008, Kyoto, Japan, September 16–19, 2008. Proceedings. Lecture Notes in Computer Science. Vol. 5257. Berlin: Springer-Verlag. pp. 1–20. (doi:10.1007/978-3-540-85780-8_1)