Poreck law

The Porezkische law ( English Poretzky's law ) is a sentence in the Boolean algebra , one of the branches of mathematics , which is named after the Russian mathematician Plato Sergejewitsch Porezki . The theorem gives a characteristic property of the zero element of a Boolean algebra.

Representation of the law

Porezki's law can be formulated as follows:

A Boolean algebra is given . Then the equivalence holds for all elements : ${\displaystyle (B,\land ,\lor ,{'},1,0)}$ ${\displaystyle a,b\in B}$

${\displaystyle a=0}$ then and only if the equation

${\displaystyle b=(a\land b^{'})\lor (a^{'}\land b)}$

is satisfied.

literature

• Joseph Gallian : Contemporary Abstract Algebra . DC Heath and Company, Lexington (Mass.), Toronto 1986, ISBN 0-669-09325-4 .
• Birkhoff - MacLane : Algebra , Chelsea, ISBN 0-8218-1646-2

Web links

• M. Barile : Poretsky's Law (MathWorld)

Remarks

1. ↑ In English-speaking countries, both “Poretzky” and “Poretsky” can be found as transcriptions of Porezki's name from Russian into English; see. Article about Porezki in the English language Wikipedia !
2. ↑ For is the complement of . ${\displaystyle b\in B}$ ${\displaystyle b^{'}}$ ${\displaystyle b}$

Individual evidence

1. ^ ^{A b} Joseph A. Gallian: Contemporary Abstract Algebra. 1986, p. 420