identity element


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identity element

[ī′den·ə‚dē ‚el·ə·mənt]
(mathematics)
The unique element e of a group where g · e = e · g = g for every element g of the group. Also known as identity.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
References in periodicals archive ?
Then (RNQ(H), [symmetry]) is an [H.sub.v]-group with identity element [bar.0] = (0, [p.summation over (i=1)] 0[T.sub.i], [r.summation over(j=1)] 0[I.sub.j], [s.summation over(k=1)] 0[F.sub.k]) if and only if (H, +) is an [H.sub.v]-group with an identity element 0.
Theorem 49 Let (Eq.) be a symmetric semi open neighbourhood of the identity element of a semi connected irresolute topological group
Now we describe a strategy of Derek for i < p such that at the endpoints of A1, A2, ..., [A.sub.i] the token will be at i different positions, also different from the identity element, which is the starting position.
We call 1 as an identity element of (m, n)-semiring (R, f, g).
Let e be the identity element of the special loop ([L.sub.M], [omicron]).
Proof: The coefficient of the identity element 1 in [A.sub.J] is 1.
A two-dimensional unital division algebra B is spanned by the identity element 1 and some element b [member of] B \ R1.
All the three 3x3 Latin groups are cyclic, that is, there is an element x such that [x.sup.3] = e, the identity element for each of these groups.
It has a compact support at {0} = ((0, 0); 0), the identity element of G, so that u [member of] U.
Vollmer & Mills, 1966)--can form a tension for the profession because individual mental health counselors may weight identity elements differently for the career path than the profession highlights in accomplishing its mission.
This shows that each and every non identity element in G is a pendent vertex in Ne(G, I).