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- W2525567447 abstract "Every (left) linear function on a subspace of a finite-dimensional vector space over a (skew) field can be extended to a (left) linear function on the whole space. This paper explores the extent to what this basic fact of linear algebra is applicable to more general structures. Semifields with a similar property imposed on linear functions are called (left) exact, and we present a complete description of such semifields. Namely, we show that a semifield $S$ is left exact if and only if $S$ is either a skew field or an idempotent semiring. In particular, our result is new even for the tropical semiring and gives a solution to the problem posed by Wilding. Also, we point out several problems that require further investigation." @default.
- W2525567447 created "2016-10-07" @default.
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- W2525567447 date "2016-09-28" @default.
- W2525567447 modified "2023-09-25" @default.
- W2525567447 title "Which semifields are exact" @default.
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