division ring

English

Noun

division ring (plural division rings)

1. (algebra) A ring with 0 ≠ 1, such that every non-zero element a has a multiplicative inverse, meaning an element x with ax = xa = 1.

Synonyms

• skew field

Hypernyms

• noncommutative ring

Hyponyms

• division algebra
• field

Translations

algebraic concept

• Czech: těleso (cs) n
• Dutch: (Belgium) lichaam (nl) n, (Netherlands) scheef lichaam n
• Finnish: jakorengas
• French: anneau à division m, corps gauche m, corps non commutatif m, corps (fr) m
• Polish: pierścień z dzieleniem m, (dated) ciało nieprzemienne n