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