different between nilpotent vs idempotent
nilpotent
English
Etymology
From nil (“not any”) +? potent (“having power”) with literal meaning “having zero power” - bearing Latin roots nil and potens.Coined in 1870, along with idempotent, by American mathematician Benjamin Peirce to describe elements of associative algebras.
Adjective
nilpotent (not comparable)
- (algebra, ring theory, of an element x of a semigroup or ring) Such that, for some positive integer n, xn = 0.
- 2012, Martin W. Liebeck, Gary M. Seitz, Unipotent and Nilpotent Classes in Simple Algebraic Groups and Lie Algebras, American Mathematical Society, page 129,
- The rest of this book is devoted to determining the conjugacy classes and centralizers of nilpotent elements in L(G) and unipotent elements in G, where G is an exceptional algebraic group of type E8,E7, E6, F4 or G2 over an algebraically closed field K of characteristic p. This chapter contains statements of the main results for nilpotent elements.
- 2012, Martin W. Liebeck, Gary M. Seitz, Unipotent and Nilpotent Classes in Simple Algebraic Groups and Lie Algebras, American Mathematical Society, page 129,
Coordinate terms
- idempotent
Derived terms
- nilpotent algebra
- nilpotent ideal
- nilpotently
- nilpotent orbit
- nilpotent semigroup
Related terms
- nilpotence
- nilpotency
- idempotent
- nullipotent
- unipotent
Translations
Noun
nilpotent (plural nilpotents)
- (algebra) A nilpotent element.
nilpotent From the web:
- what nilpotent element
- what is nilpotent matrix
- what is nilpotent matrix with example
- what is nilpotent group
- what is nilpotent series
- what is a nilpotent subalgebra
idempotent
English
Etymology
Latin roots, idem (“same”) +? potent (“having power”) – literally, “having the same power”.
Coined 1870 by American mathematician Benjamin Peirce in context of algebra.
Pronunciation
- (US) IPA(key): /a?.d?m?po?.t?nt/, /?.d?m?po?.t?nt/
Adjective
idempotent (not comparable)
- (mathematics, computing) Said of a function: describing an action which, when performed multiple times on the same subject, has no further effect on its subject after the first time it is performed.
- A projection operator is idempotent.
- (mathematics) Said of an element of an algebraic structure with a binary operation (such as a group or semigroup): when the element operates on itself, the result is equal to itself.
- Every finite semigroup has an idempotent element.
- Every group has a unique idempotent element: namely, its identity element.
- (mathematics) Said of a binary operation: such that all of the distinct elements it can operate on are idempotent (in the sense given just above).
- Since the AND logical operator is commutative, associative, and idempotent, then it distributes with respect to itself.
- (mathematics) Said of an algebraic structure: having an idempotent operation (in the sense above).
Usage notes
See the Usage notes section of nullipotent.
Coordinate terms
- nilpotent
- nullipotent
Related terms
- idempotence
- nilpotent
- nullipotent
- unipotent
Translations
Noun
idempotent (plural idempotents)
- (mathematics) An idempotent element.
- (mathematics) An idempotent structure.
References
- “idempotent” at FOLDOC
German
Pronunciation
Adjective
idempotent
- idempotent
Swedish
Adjective
idempotent
- idempotent
Turkish
Adjective
idempotent
- idempotent
idempotent From the web:
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