Semifield

In mathematics, a semifield is an algebraic structure with two binary operations, addition and multiplication, which is similar to a field, but with some axioms relaxed. There are at least two conflicting conventions of what constitutes a semifield.

A semifield D is called right (resp. left) primitive if it has an element w such that the set of nonzero elements of D* is equal to the set of all right (resp. left) principal powers of w.

We only give examples of semifields in the second sense, i.e. additive semigroups with distributive multiplication. Moreover, addition is commutative and multiplication is associative in our examples.

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