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Rings

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,â‹…R,\cdotR,â‹…is a monoid (group without the inverse axiom) with identity111.

  • Distributivity:

// ideals, diff types of domains

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