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Axiom: Axiom of Distributivity

We say that the binary operation “\(\cdot\)” is distributive over the binary operation “\( + \)”, if the distributivity law
\[(x+y)\cdot z=x\cdot z + y\cdot z\quad\quad\text{“right-distributivity property”}\]
and
\[x\cdot (y+z)=x\cdot y + x\cdot z\quad\quad\text{“left-distributivity property”}\]
holds for any three elements \(x,y,z\) of an algebraic structure, in which these two operations are defined and for which the law is postulated.

| | | | | created: 2014-06-12 22:42:31 | modified: 2015-10-18 09:12:36 | by: bookofproofs | references: [577]


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Bibliography (further reading)

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

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