Field

A commutative ring with unity in which every nonzero element has a multiplicative inverse; it supports addition, subtraction, multiplication and division (by nonzero elements) and provides the canonical scalar domains for vector spaces and many algebraic constructions.

A commutative ring with unity in which every nonzero element has a multiplicative inverse; equivalently, a set with two operations forming an abelian additive group and a multiplicative abelian group on nonzero elements.

A commutative ring with unity in which every nonzero element has a multiplicative inverse; equivalently, a commutative ring whose nonzero elements form an abelian group under multiplication.

A commutative division ring: an associative ring with unity in which multiplication is commutative and every nonzero element has a multiplicative inverse.