Higher rank graph -algebras.
Kumjian, Alex, Pask, David (2000)
The New York Journal of Mathematics [electronic only]
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Kumjian, Alex, Pask, David (2000)
The New York Journal of Mathematics [electronic only]
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Matsumoto, Kengo (2002)
Documenta Mathematica
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Bates, Teresa, Pask, David, Raeburn, Iain, Szymański, Wojciech (2000)
The New York Journal of Mathematics [electronic only]
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Pask, David, Quigg, John, Raeburn, Iain (2004)
The New York Journal of Mathematics [electronic only]
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Tiang Poomsa-ard (2000)
Discussiones Mathematicae - General Algebra and Applications
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Graph algebras establish a connection between directed graphs without multiple edges and special universal algebras of type (2,0). We say that a graph G satisfies an identity s ≈ t if the correspondinggraph algebra A(G) satisfies s ≈ t. A graph G is called associative if the corresponding graph algebra A(G) satisfies the equation (xy)z ≈ x(yz). An identity s ≈ t of terms s and t of any type τ is called a hyperidentity of an algebra A̲ if whenever the operation symbols occurring in s...
Johnson, Matthew (2005)
The New York Journal of Mathematics [electronic only]
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Jung Rae Cho, Jeongmi Park, Yoshio Sano (2014)
Czechoslovak Mathematical Journal
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The notion of travel groupoids was introduced by L. Nebeský in 2006 in connection with a study on geodetic graphs. A travel groupoid is a pair of a set and a binary operation on satisfying two axioms. We can associate a graph with a travel groupoid. We say that a graph has a travel groupoid if the graph associated with the travel groupoid is equal to . Nebeský gave a characterization of finite graphs having a travel groupoid. In this paper, we study travel groupoids on infinite...
Paul S. Muhly, Baruch Solel (1989)
Journal für die reine und angewandte Mathematik
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Ladislav Nebeský (2006)
Czechoslovak Mathematical Journal
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In this paper, by a travel groupoid is meant an ordered pair such that is a nonempty set and is a binary operation on satisfying the following two conditions for all : Let be a travel groupoid. It is easy to show that if , then if and only if . We say that is on a (finite or infinite) graph if and Clearly, every travel groupoid is on exactly one graph. In this paper, some properties of travel groupoids on graphs are studied.
Hirshberg, Ilan (2002)
The New York Journal of Mathematics [electronic only]
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