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## Definition: Commutative (Unit) Ring

A ring $$(R, +,\cdot)$$ is called a commutative ring, if the binary operation “$$\cdot$$” is commutative, i.e. if $$(R,\cdot)$$ is a commutative semigroup.

A unit ring $$(R, +,\cdot)$$ is called a commutative unit ring, if in addition $$(R,\cdot)$$ as a neutral element of the operation “$$\cdot$$”, i.e. if $$(R,\cdot)$$ is a commutative monoid.

| | | | | created: 2014-09-17 18:52:02 | modified: 2016-09-04 21:16:15 | by: bookofproofs | references: [696], [6907]

## 1.Definition: Multiplicative System

### CC BY-SA 3.0

[6907] Brenner, Prof. Dr. rer. nat., Holger: “Various courses at the University of Osnabrück”, https://de.wikiversity.org/wiki/Wikiversity:Hochschulprogramm, 2014