Which semifields are exact?

[摘要] 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. (C) 2017 Elsevier Inc. All rights reserved.

[发布日期] 2017-12-15

[关键词] Exact semiring;Idempotent semiring;Semifield