• Honam Mathematical Journal
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• v.27 no.4
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• pp.595-602
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• 2005

Comtrans algebras are modules equipped with two trilinear operations: a left alternative commutator and a translator satisfying the Jacobi identity, the commutator and translator being connected by the so-called comtrans identity. These identities have analogues for trilinear forms. On a given vector space, the set of all comtrans algebra structures itself forms a vector space. In this paper, the dimension of the space of comtrans algebra structures on a finite-dimensional vector space is determined.

• Journal of the Chungcheong Mathematical Society
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• v.26 no.4
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• pp.843-852
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• 2013

The characteristic connection is a good substitute for Levi-Civita connection in studying non-integrable geometries. In this paper we consider the homogeneous space $U(3)/(U(1){\times}U(1){\times}U(1))$ with a one-parameter family of Hermitian structures. We prove that the one-parameter family of Hermtian structures admit a characteristic connection. We also compute the torsion of the characteristic connecitons.

• Honam Mathematical Journal
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• v.33 no.4
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• pp.535-546
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• 2011

Using $\mathcal{N}$-structures, the notion of an $\mathcal{N}$-ideal in a prelogic is introduced. Characterizations of an $\mathcal{N}$-ideal are discussed. Conditions for an $\mathcal{N}$-structure to be an $\mathcal{N}$-ideal are provided.

• Journal of the Chungcheong Mathematical Society
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• v.27 no.2
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• pp.205-210
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• 2014

The author with C. H. Kim and Y. Lee constructed infinite families of elliptic curves over cubic number fields K with prescribed torsion groups which occur infinitely often. In this paper, we examine the Galois structures of such cubic number fields K for the families of elliptic curves with cyclic torsion.

• Journal of the Korean Mathematical Society
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• v.46 no.4
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• pp.859-893
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• 2009

In this article, we will characterize structures of geometric quotient orbifolds of G-manifold of genus two where G is a finite group of orientation preserving diffeomorphisms using the idea of handlebody orbifolds. By using the characterization, we will deduce the candidates of possible non-hyperbolic geometric quotient orbifolds case by case using W. Dunbar's work. In addition, if the G-manifold is compact, closed and the quotient orbifold's geometry is hyperbolic then we can show that the fundamental group of the quotient orbifold cannot be in the class D.

• Journal of the Chungcheong Mathematical Society
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• v.22 no.3
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• pp.587-591
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• 2009

The structure of a TL-subgroup can be understood from the representations of the TL-sub group as meets of TL-subgroups containing the TL-subgroup. Indeed, the structure of the meet of TL-subgroups can easily be obtained from the structures of the TL-subgroups and the structures of the TL-subgroups may be more simple than the structure of the meet. In this paper, we discuss meet-reducibility of TL-subgroups.

• Communications of the Korean Mathematical Society
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• v.27 no.1
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• pp.15-22
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• 2012

Using $\mathcal{N}$-structures, the notion of an $\mathcal{N}$-essence in a sub-traction algebra is introduced, and related properties are investigated. Relations among an $\mathcal{N}$-ideal, an $\mathcal{N}$-subalgebra and an $\mathcal{N}$-essence are investigated.

• Honam Mathematical Journal
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• v.31 no.4
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• pp.497-504
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• 2009

We introduce the concepts of M-preclosed graph and M$^*$-preopen mapping on spaces with minimal structures and investigate some properties of M$^*$-preopen mapping. We also investigate the relationships between M-precontinuous mappings and several types of m-compactness.

• Journal of the Chungcheong Mathematical Society
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• v.31 no.4
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• pp.421-427
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• 2018

The aim of this study is to investigate the prolongations of G-structures immersed in the generalized almost r-contact structure on a manifold M to its tangent bundle T(M) of order 2. Moreover, theorems on Hsu structure, integrability and (${F\limits^{\circ}},\;{{\xi}\limits^{\circ}}{{\omega}\limits^{\circ}}_p,\;a,\;{\epsilon}$)-structure have been established.

• Communications of the Korean Mathematical Society
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• v.36 no.3
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• pp.623-639
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• 2021

We define a new algebraic structure called Legendrian racks or racks with Legendrian structure, motivated by the front-projection Reidemeister moves for Legendrian knots. We provide examples of Legendrian racks and use these algebraic structures to define invariants of Legendrian knots with explicit computational examples. We classify Legendrian structures on racks with 3 and 4 elements. We use Legendrian racks to distinguish certain Legendrian knots which are equivalent as smooth knots.