\input zb-basic
\input zb-ioport
\iteman{io-port 06002417}
\itemau{Guan, Xuechong; Li, Yongming}
\itemti{On the order relations over projection problems.}
\itemso{J. Shaanxi Norm. Univ., Nat. Sci. Ed. 39, No. 1, 5-9 (2011).}
\itemab
Summary: The projection problem on valuation algebras is introduced. The solution-order and the problem-order on projection problems are defined. The relationships between these order relations on projection problems are studied. It is proved that a mapping between two semirings preserves the problem-order if and only if it is monotonic. It is shown that a surjective mapping between two semirings preserves the solution-order on projection problems if and only if it is a semiring homomorphism.
\itemrv{~}
\itemcc{}
\itemut{valuation algebra; projection problem; semiring homomorphism; order}
\itemli{}
\end