identity element

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identity element

n.
The element of a set of numbers that when combined with another number in a particular operation leaves that number unchanged. For example, 0 is the identity element under addition for the real numbers, since if a is any real number, a + 0 = 0 + a = a. Similarly, 1 is the identity element under multiplication for the real numbers, since a × 1 = 1 × a = a. Also called unity.
American Heritage® Dictionary of the English Language, Fifth Edition. Copyright © 2016 by Houghton Mifflin Harcourt Publishing Company. Published by Houghton Mifflin Harcourt Publishing Company. All rights reserved.
ThesaurusAntonymsRelated WordsSynonymsLegend:
Noun1.identity element - an operator that leaves unchanged the element on which it operates; "the identity under numerical multiplication is 1"
operator - (mathematics) a symbol or function representing a mathematical operation
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References in periodicals archive ?
[9] studied the concept of intra-regular LA-semihypergroups with pure left identity and Yousafzai and Corsini [10] considered some characterization problems in LA-semihypergroups.
This left identity has different to classical liberalism final authority that decides about criteria of rationality and decide how an individual has to think and act.
Nagle points to the revival of a class-based economic left as a way out of the clash of right and left identity politics.
An AG-groupoid may or may not contain a left identity. The left identity of an AG-groupoid permits the inverses of elements in the structure.
An element x [member of] H is called a left identity (resp., pure left identity) if for all x [member of] H, x [member of] e [omicron] x (resp., x = e [omicron] x).
One may wonder, however, whether labour unions, only occasionally mentioned in the study, but known in the US for their educational and cultural activities, should not have been recognized as an important presence of working-class experience in the making of the Jewish Canadian left identity.
In addition to this, if it contains a left identity, then it satisfies the famous Jordan identity and the generalized Jordan identity.
An LA-semigroup S can have left identity e (unique) i.e ea = a for all a [member of] S but it cannot have a right identity because if it has, then S becomes a commutative semigroup.
In an AG -groupoid S with left identity, the paramedial law holds
Not only the future of existing Left parties but also Turkey's hopes to consolidate its post-authoritarian democracy depend on a successful negotiation for a new Left identity in the aftermath of Gezi Park protests.
We have shown that the set of all fuzzy interior ideals of a left regular ordered LA -semigroup with left identity forms a commutative monoid.