Ring ↩

aliases: []
shorthands: {}
created: 2022-02-16 14:29:31
modified: 2022-02-16 14:50:11

Axioms

Operations: summation , subtraction , multiplication .

1. Abelian group: with the neutral element
2. Multiplication is associative:
3. Distributive: and

Optional properties/axioms:

• Commutative: (this is usually assumed by default)
• The following identity with (multiplicative identity):
  (no consensus for being a default, see Discussion of the multiplicative identity in rings)

Notes

• Comparison of group action and ring action

Examples

• integer numbers
• real numbers
• complex numbers
• polynomial rings
• matrix rings
• Gaussian integers: