identity element


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Related to identity element: Inverse element
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  • noun

Synonyms for identity element

an operator that leaves unchanged the element on which it operates

References in periodicals archive ?
Then (RNQ(H), [symmetry]) is an [H.sub.v]-semigroup 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]-semigroup with identity element 0.
Let M is a W*-algebra and A [??] M a commutative W*-subalgebra of M containing the identity element of M.
Let R be a commutative Q-algebra with the identity element 1.
Definition 10 Semi component of an identity element of an irresolute topological group (Eq.) is the largest semi connected subset of that contains the identity element e of the group (Eq.).
(5) As identity elements must be unique, the operation does not have an identity; however, in order for the operation to have no effect on an individual input, the other 'input' must be a person (or robot!) with the same exact brain.
We suppose that the token is at the identity element in the beginning of the game.
Finally, in relation to the dynamics of the visual identity element, it remains static in 62.7% of the cases, while 11.8% incorporates some type of movement.
We call 0 as an identity element of (m, n)-semiring (R, f, g).
There is an open relatively compact neighborhood O of the identity element of G with [O.sup.2] [subset or equal to] U.
In order to examine differences between the three samples of ventures in our post hoc analysis, we conducted a MANOVA test and accompanying univariate F-tests on each of the identity elements, comparing FastCompany, Skoll, and Inc.
Furthermore, if there exists a unique element e = [e.sub.[rho]] = [e.sub.[lambda]] in L called the identity element such that for all x in L, x * e = e * x = x, (L,*) is called a loop.
Given any monoid T, that is, a set with an associative multiplication and an identity element, we define a preorder [less than or equal to] as follows.
"Although Taffs Well have been superb in accommodating us, training at Penydarren will give the players an identity element to the whole thing.
A real finite-dimensional division algebra is power associative if and only if it is quadratic, that is, if it has an identity element 1 [not equal to] 0 and the set {1,x,[x.sub.2]} is linearly dependent for all x (this follows from the fact that every finite-dimensional power-associative division algebra has an identity element [30, Lemma 5.3]).
of New Mexico) call the graphs identify graphs, because the main role in obtaining them is the identity element of the group.