The Weyl

groupoid of a Nichols algebra of diagonal type.

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.