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Idempotence

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A property of a binary operation. For the logical operation of conjunction ($\wedge$) and disjunction ($\vee$) is expressed by the following identities: $$ a \wedge a = a\ \ \text{and}\ \ a \vee a = a \ . $$

A general binary operation $\star$ is idempotent if the identity $$ a \star a = a $$ is valid in the given algebraic system: that is, every element $a$ of the given system is an idempotent.

References

[a1] R.H. Bruck, "A survey of binary systems" Ergebnisse der Mathematik und ihrer Grenzgebiete. Neue Folge. 20 Springer (1958) Zbl 0081.01704
How to Cite This Entry:
Idempotence. Encyclopedia of Mathematics. URL: http://www.encyclopediaofmath.org/index.php?title=Idempotence&oldid=39755