groupoid

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groupoid

(ˈɡruːpɔɪd)
n
(Mathematics) maths an algebraic structure consisting of a set with a single binary operation acting on it
References in periodicals archive ?
It does not discuss partial actions of topological groups, focusing instead on discrete groups, and also omits the computation of k-theory groups of partial crossed product algebras, twisted partial actions and projective partial representations, detailed discussion of partial actions and inverse semigroups, and the relationship between partial actions and groupoids.
Kandasamy and Smarandache [7] introduced the philosophical algebraic structures, in particular, Neutrosophic algebraic structures with illustrations and examples in 2006 and initiated the new way for the emergence of a new class of structures, namely, Neutrosophic groupoids, Neutrosophic groups, Neutrosophic rings etc.
A number of the neutrosophic algrebraic structures introduced and considered include neutrosophic fields, neutrosophic vector spaces, neutrosophic groups, neutrosophic bigroups, neutrosophic N-groups, neutrosophic bisemigroups, neutrosophic N-semigroup, neutrosophic loops, neutrosophic biloops, neutrosophic N-loop, neutrosophic groupoids, neutrosophic bigroupoids and neutrosophic AG-groupoids.
They begin with basic definitions and then address three-dimensional topology, distributive groupoids, the Jones-Kauffman polynomial atoms, Khovanov homology, virtual braids, Vassilierv's invariants and framed graphs, parity, and theory of graph-links.
Kandasamy defined new classes of Smarandache groupoids using [Z.
The 11 chapters in this volume present a varied range of research in the study of group theory in mathematics and other fields, including the application of symmetry analysis to the description of ordered structures in crystals, a survey of Lie group analysis, and discussion of graph groupoids and representations.
Martfnez: A survey of Lagrangian mechanics and control on Lie algebroids and groupoids, Int.
Therefore abelian groups are completely characterized as subtractive groupoids.
The role of groupoids in partial actions was first pointed out by F.
Some of the neutrosophic algebraic structures introduced and studied including neutrosophic fields, neutrosophic vector spaces, neutrosophic groups, neutrosophic bigroups, neutrosophic N-groups, neutrosophic bisemigroups, neutrosophic N-semigroup, neutrosophic loops, neutrosophic biloops, neutrosophic N-loop, neutrosophic groupoids, neutrosophic bigroupoids and neutrosophic AG-groupoids.
He also describes a duality theory for hyperbolic groupoids and shows that for every hyperbolic groupoid, there is a naturally defined dual groupoid acting on the Gromov boundary of a Cayley graph of the original groupoid.