Homotopy Type Theory commutative Heyting division ring > history (Rev #1)

Definition

A commutative Heyting division ring is a Heyting division ring $(A, +, -, 0, \cdot, 1, #)$ with a commutative identity for $\cdot$:

Properties

Every commutative Heyting division ring is a commutative Heyting reciprocal ring.

Examples

• The rational numbers are a commutative Heyting division ring.

• Every commutative discrete division ring is a commutative Heyting division ring.

• Every commutative Heyting reciprocal ring is a commutative Heyting division ring, and thus every Heyting field is a commutative Heyting division ring.

See also

• commutative ring

• commutative division ring