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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

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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

Bibliography (further reading)

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

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