**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

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

[696] **Kramer Jürg, von Pippich, Anna-Maria**: “Von den natürlichen Zahlen zu den Quaternionen”, Springer-Spektrum, 2013

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