# ring

# ring (2)

( < Hilberti *Zahlring*, "arvuring")

**olemus**

aditiivne Abeli rühm, kus lisaks liitmisele

on ka korrutamine (*), mis on

assotsiatiivne, st *a**(*b***c*)=(*a***b*)**c* ja

distributiivne liitmise suhtes, st
*a**(*b*+*c*) = *a***b* + *a***c* ja (*b*+*c*)**a* = *b***a* + *c***a*

Wiktionary:
*1. (algebra) an algebraic structure which consists of a set with two binary operations: an additive operation and a multiplicative operation, such that the set is an abelian group under the additive operation, a monoid under the multiplicative operation, and such that the multiplicative operation is distributive with respect to the additive operation
2. (algebra) an algebraic structure as above, but only required to be a semigroup under the multiplicative operation, that is, there need not be a multiplicative identity element*

**näiteid**

täisarvude hulk tavalise liitmise ja korrutamisega

= the set of integers with ordinary addition and multiplication

**ülevaateid**

https://en.wikipedia.org/wiki/Ring_(mathematics)

https://en.wikipedia.org/wiki/Ring_theory

https://en.wikipedia.org/wiki/Prime_ring

https://jeremykun.com/2013/04/30/rings-a-primer/

http://mathworld.wolfram.com/Ring.html