Last updated 3 years ago
A setRRRwith two binary operations +,⋅:R×R→R+,\cdot:R\times R\to R+,⋅:R×R→Ris a ring if the following holds:
R,+R,+R,+is a commutative group with identity 000
R,⋅R,\cdotR,⋅is a monoid (group without the inverse axiom) with identity111.
Distributivity: a(b+c)=ab+ac,(a+b)c=ac+bca(b+c)=ab+ac,(a+b)c=ac+bca(b+c)=ab+ac,(a+b)c=ac+bc
// ideals, diff types of domains
