# groupoid

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## groupoid

[′grü‚pȯid]
(mathematics)
A set having a binary relation everywhere defined.
References in periodicals archive ?
A neutrosophic groupoid satisfying the left invertive law is called a neutrosophic left almost semigroup and is abbreviated as neutrosophic LA-semigroup.
A Smarandache groupoid G is a groupoid which has a proper subset S [subset] G which is a semi-group under the operation of G.
This operation over which the various 'directions' are taken (1) subsequently determines the holonomy of the system through an error-correction network--a broader scale geometric representation of transitional phases in which the broken symmetries may be expressed in terms of holonomy groups that collectively, via disjoint union, form a holonomy groupoid, a structure which in principle can be given explicitly.
A subset I of an right modular groupoid S is called left (right) ideal of S if SI [subset or equal to] I(IS [subset or equal to] I).
Thus, gyr[u, v] of the definition in (4) is the gyroautomorphism of the Einstein groupoid ([R.
Thus any abelian group must be a subtractive groupoid.
In the same section we show that, for the case of a partial action of a finite group on a finite set, the partial skew group algebra is isomorphic to the algebra of the groupoid associated to that partial action.
Rosenfeld [3] was the first who consider the case of a groupoid in terms of fuzzy sets.
By Theorem 5, P is a groupoid, where the inverse of a morphism [P] : T [right arrow] S is [[P.
Define a binary operation (*) on L: if x * y [member of] L for all x,y [member of] L, (L,*) is called a groupoid.
For example one may think of X/G as the groupoid whose set of objects is X and with morphisms given by X/G(a, b) = {g [member of] G|ga = b} for a,b [member of] G.

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