semi-fieldn.

Etymology: semi- prefix 2c(a).Previous versions of the OED give the stress as: ˈsemi-field.

Mathematics.

Used variously to denote a set, together with operations answering to addition and multiplication, that has certain specified properties of a field but not all of them.

ΚΠ

1923 Ann. Math. 24 240 A set D which satisfies these postulates will be called a semi-field.

1966 Math. Rev. 31 39/2 A semifield is essentially an algebraic structure which satisfies all field axioms except perhaps associativity and commutativity of multiplication; the more customary terminologies are ‘division ring’ (not necessarily associative) and ‘distributive quasifield’.

This entry has not yet been fully updated (first published 1986; most recently modified version published online June 2019).

单词	semi-field
释义	semi-fieldn. Etymology: semi- prefix 2c(a).Previous versions of the OED give the stress as: ˈsemi-field. Mathematics. Used variously to denote a set, together with operations answering to addition and multiplication, that has certain specified properties of a field but not all of them. ΚΠ 1923 Ann. Math. 24 240 A set D which satisfies these postulates will be called a semi-field. 1966 Math. Rev. 31 39/2 A semifield is essentially an algebraic structure which satisfies all field axioms except perhaps associativity and commutativity of multiplication; the more customary terminologies are ‘division ring’ (not necessarily associative) and ‘distributive quasifield’. This entry has not yet been fully updated (first published 1986; most recently modified version published online June 2019). < n.1923
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