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Definition: Field

A commutative unit ring $R$ (with the multiplicative neutral element $1$) is called a field, if $R$ is not the zero ring and every element \(x\in R\) with $x\neq 0$ ($0$ being the additive neutral element) has a multiplicative inverse.

“Unfolding” all definitions, a field fulfills the following axioms:

Notes

| | | | | created: 2014-03-28 21:11:15 | modified: 2020-07-03 18:14:40 | by: bookofproofs | references: [577], [6907]

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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)

[577] Knauer Ulrich: “Diskrete Strukturen – kurz gefasst”, Spektrum Akademischer Verlag, 2001