Idempotence
From Encyclopedia of Mathematics
The printable version is no longer supported and may have rendering errors. Please update your browser bookmarks and please use the default browser print function instead.
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://encyclopediaofmath.org/index.php?title=Idempotence&oldid=39755
Idempotence. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Idempotence&oldid=39755