===== Ring =====
==== Set ====
| @#55CCEE: context     | @#55CCEE: $\langle X,+ \rangle \in \mathrm{AbelianGroup}(X)$ |
| @#FFBB00: definiendum | @#FFBB00: $\langle X,+,* \rangle\in\mathrm{it}$ |
| @#FFFDDD: for all     | @#FFFDDD: $a,b,c\in X$ |
| @#55EE55: postulate   | @#55EE55: $(a*b)*c=a*(b*c)$ |
| @#55EE55: postulate   | @#55EE55: $a*(b+c)=(a*b)+(a*c)$ |
| @#55EE55: postulate   | @#55EE55: $(b+c)*a=(b*a)+(c*a)$ |

==== Discussion ====

One might call the commutative group operation "$+$" the //addition// and the other one "$*$" the //multiplication//. In a [[unital ring]], the latter has an identity too.

One generally calls $X$ the ring, i.e. the set where the operations "$+$" and "$*$" are defined on.
=== Reference ===
Wikipedia: [[http://en.wikipedia.org/wiki/Ring_%28mathematics%29|Ring]]

{{ueberall_blumen_und_girlanden_halb_zerknuellt.jpg?X600 }} /* Claudia Krizmanits 2014 */

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=== Subset of ===
[[Semiring]]
=== Context ===
[[Abelian group]]