• Korean Journal of Mathematics
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• v.13 no.1
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• pp.13-18
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• 2005

Recently, Kehayopulu and Tsingelis studied for prime ideals of groupoids-ordered groupoids. In this paper, we give some results on prime left(right) ideals of groupoid-ordered groupoid. These results are generalizations of their results.

• Communications of the Korean Mathematical Society
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• v.11 no.4
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• pp.925-932
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• 1996

On certain groupoids called LIR-groupoids, one can define abstract definitions of continuity and differentiation of functions. Many properties of this abstract continuity and differentiation have analogy to the ordinary continuity and differentiation of real-valued functions.

• Korean Journal of Mathematics
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• v.13 no.2
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• pp.217-221
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• 2005

Kehayopulu and Tsingelis [2] studied prime ideals of groupoids. Also the author studied prime left (right) ideals of groupoids. In this paper, we give some results on prime bi-ideals of groupoids.

• Korean Journal of Mathematics
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• v.27 no.1
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• pp.151-163
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• 2019

The aim of this paper is to consider the categorical equivalence between crossed modules within groupoids and 2-groupoids; and then relate normality and quotient in these two categories.

• Korean Journal of Mathematics
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• v.32 no.1
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• pp.27-42
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• 2024

In this paper we define generalized double group-groupoids and crossed modules over generalized group-groupoids. Also we prove that these algebraic structures are categorically equivalent.

• Bulletin of the Korean Mathematical Society
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• v.54 no.4
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• pp.1373-1386
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• 2017

In this paper, we introduce and explore suggested notions of 'above', 'below' and 'between' in general groupoids, Bin(X), as well as in more detail in several well-known classes of groupoids, including groups, semigroups, selective groupoids (digraphs), d/BCK-algebras, linear groupoids over fields and special cases, in order to illustrate the usefulness of these ideas. Additionally, for groupoid-classes (e.g., BCK-algebras) where these notions have already been accepted in a standard form, we look at connections between the several definitions which result from our introduction of these ideas as presented in this paper.

• Journal of the Korean Mathematical Society
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• v.57 no.2
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• pp.383-399
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• 2020

Following Matsumoto's definition of continuous orbit equivalence for one-sided subshifts of finite type, we introduce the notion of orbit equivalence to canonically associated dynamical systems, called the limit dynamical systems, of self-similar groups. We show that the limit dynamical systems of two self-similar groups are orbit equivalent if and only if their associated Deaconu groupoids are isomorphic as topological groupoids. We also show that the equivalence class of Cuntz-Pimsner groupoids and the stably isomorphism class of Cuntz-Pimsner algebras of self-similar groups are invariants for orbit equivalence of limit dynamical systems.

• East Asian mathematical journal
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• v.22 no.2
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• pp.215-221
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• 2006

On a groupoid satisfying the Austin's identity, every n-ary linear term is essentially n-ary. That is, if a term has no variables appearing more than once, then the term depends on every variable it involves.

• East Asian mathematical journal
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• v.35 no.1
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• pp.17-22
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• 2019

A travel groupoid is a pair (V, ${\ast}$) of a set V and a binary operation ${\ast}$ on V satisfying two axioms. For a travel groupoid, we can associate a graph in a certain manner. For a given graph G, we say that a travel groupoid (V, ${\ast}$) is on G if the graph associated with (V, ${\ast}$) is equal to G. There are some results on the classification of travel groupoids which are on a given graph [1, 2, 3, 9]. In this article, we introduce the notion of vertex-indexed partition systems on a graph, and classify the travel groupoids on the graph by the those vertex-indexed partition systems.

• Kyungpook Mathematical Journal
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• v.16 no.1
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• pp.7-20
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• 1976