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- W4300771503 abstract "The fundamental theorem of symmetric polynomials over rings is a classical result which states that every unital commutative ring is fully elementary, i.e. we can express symmetric polynomials with elementary ones in a unique way. The result does not extend directly to polynomials over semirings, but we do have analogous results for some special semirings, for example, the tropical, extended and supertropical semirings. These all fall into a larger class of upper-bound semirings. In this paper we extend the known results and give a complete characterization of fully elementary upper-bound semirings. We further improve this characterization statement in the case of linearly ordered upper-bound semirings." @default.
- W4300771503 created "2022-10-04" @default.
- W4300771503 creator A5019442939 @default.
- W4300771503 creator A5044763894 @default.
- W4300771503 date "2018-01-26" @default.
- W4300771503 modified "2023-10-14" @default.
- W4300771503 title "Symmetric Polynomials in Upper-bound Semirings" @default.
- W4300771503 doi "https://doi.org/10.48550/arxiv.1801.08882" @default.
- W4300771503 hasPublicationYear "2018" @default.
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