identity element
Noun
This text is extracted from the Wiktionary and it is available under the CC BY-SA 3.0 license | Terms and conditions | Privacy policy 0.002
Noun
identity element (plural identity elements)
- (algebra) An element of an algebraic structure which when applied, in either order, to any other element via a binary operation yields the other element.
- 1990, Daniel M. Fendel, Diane Resek, Foundations of Higher Mathematics, Volume 1, Addison-Wesley, page 269 ↗,
- Therefore the number 0 is not considered an identity element for subtraction, even though x - 0 = x for all x, since 0 - x\ne x.
- 2003, Houshang H. Sohrab, Basic Real Analysis, Birkhäuser, page 17 ↗,
- Let (G,\cdot) be a group. Then the identity element e\in G is unique. […]
- Proof. If e and e' are both identity elements, then we have ee' = e since e' is an identity element, and ee' = e' since e is an identity element. Thus
- e = ee' = e'.
- 2015, Martyn R. Dixon, Leonid A. Kurdachenko, Igor Ya. Subbotin, An Introduction to Essential Algebraic Structures, Wiley, page 41 ↗,
- Sometimes, to avoid ambiguity, we may use the notation e_M for the identity element of M.
- If multiplicative notation is used then we use the term identity element, and often use the notation 1, or 1_M, for the neutral element e.
- 1990, Daniel M. Fendel, Diane Resek, Foundations of Higher Mathematics, Volume 1, Addison-Wesley, page 269 ↗,
- (element that when applied with a binary operation leaves any other element unchanged) identity, neutral element
- Italian: elemento neutro
- Russian: то́ждество
- Spanish: elemento neutro
This text is extracted from the Wiktionary and it is available under the CC BY-SA 3.0 license | Terms and conditions | Privacy policy 0.002