left identity


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left identity

[¦left i′den·ə·dē]
(mathematics)
In a set in which a binary operation · is defined, an element e with the property e · a = a for every element a in the set.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
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On intra-regular left almost semihypergroups with pure left identity. J.
Let f be an ([member of], [member of] [Vq.sub.k])-fuzzy left hyperideal of an ordered LA-semihypergroup H with pure left identity e.
Let H be an ordered LA-semihypergroup with pure left identity. If f is an ([member of], [member of] [Vq.sub.k])-fuzzy subset of H and g is an ([member of], [member of] [Vq.sub.k])-fuzzy left hyperideal of H, then f x g is an ([member of], [member of] [Vq.sub.k])-fuzzy left hyperideal of H.
From the discussion above, it is easy to conclude that this nonassociative structure with left identity has a closed connection with a commutative semigroup.
If U is a left almost alternative algebra that contains a left identity e, then U becomes commutative and associative with identity.
Example 2.1 Let S = (1,2,3} with binary operation "*" is an LA-semigroup with left identity 3 and has the following Calley's table:
Lemma 2.3: If N(B) is a neutrosophic bi-ideal of a neutrosophic LA-semigroup N(S) with left identity e + eI, then (([x.sub.1] + I[y.sub.1])N(B))([x.sub.2] + I[y.sub.2]) is also a neutrosophic bi-ideal of N(S), for any [x.sub.1] + I[y.sub.1] and [x.sub.2] + I[y.sub.2] in N(S).
A neutrosophic AG-groupoid N(S] with neutrosophic left identity becomes a Neutrosophic semigroup N(S) under new binary operation "o" defined as
An -semigroup may or may not contain a left identity. The left identity of an -semigroup allow us to introduce the inverses of elements in an -semigroup.
Similarly if G is an AG-groupoid with left identity e then,
(3) A hypotopological lea A has a bai if and only if (A", []) has a right identity and (A", <>) has a left identity.
An ideal P of an LA-semigroup S with left identity e is called prime ideal if AB [subset or equal to] P implies either