Rings

A setRRwith two binary operations +,:R×RR+,\cdot:R\times R\to Ris a ring if the following holds:

  • R,+R,+is a commutative group with identity 00

  • R,R,\cdotis a monoid (group without the inverse axiom) with identity11.

  • Distributivity: a(b+c)=ab+ac,(a+b)c=ac+bca(b+c)=ab+ac,(a+b)c=ac+bc

// ideals, diff types of domains