• Bulletin of the Korean Mathematical Society
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• v.60 no.1
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• pp.203-223
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• 2023

A generalized torsion element is an obstruction for a group to admit a bi-ordering. Only a few classes of hyperbolic knots are known to admit such an element in their knot groups. Among twisted torus knots, the known ones have their extra twists on two adjacent strands of torus knots. In this paper, we give several new families of hyperbolic twisted torus knots whose knot groups have generalized torsion. They have extra twists on arbitrarily large numbers of adjacent strands of torus knots.

• Journal of the Korean Mathematical Society
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• v.41 no.2
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• pp.369-378
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• 2004

A canonical Finsler connection Nr is defined by a generalized Finsler structure called a (G, N)-structure, where G is a generalized Finsler metric and N is a nonlinear connection given in a differentiable manifold, respectively. If NT is linear, then the(G, N)-structure has a linearity in a sense and is called Berwaldian. In the present paper, we discuss what it means that NT is with a vanishing hv-torsion: ${P^{i}}\;_{jk}\;=\;0$ and introduce the notion of a stronger type for linearity of a (G, N)-structure. For important examples, we finally investigate the cases of a Finsler manifold and a Rizza manifold.

• Honam Mathematical Journal
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• v.31 no.4
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• pp.601-609
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• 2009

The notion of generalized derivations of a BCI-algebra is introduced, and some related properties are investigated. Also, the concept of a torsion free BCI-algebra is introduced and some properties are discussed.

• Bulletin of the Korean Mathematical Society
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• v.51 no.6
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• pp.1579-1589
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• 2014

We study the Dirac spectrum on compact Riemannian spin manifolds M equipped with a metric connection ${\nabla}$ with skew torsion $T{\in}{\Lambda}^3M$ in the situation where the tangent bundle splits under the holonomy of ${\nabla}$ and the torsion of ${\nabla}$ is of 'split' type. We prove an optimal lower bound for the first eigenvalue of the Dirac operator with torsion that generalizes Friedrich's classical Riemannian estimate.

• Bulletin of the Korean Mathematical Society
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• v.46 no.3
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• pp.553-565
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• 2009

In this paper we prove that every generalized Jordan triple higher derivation on a 2-torsion free semiprime ring is a generalized higher derivation. This extend the main result of [9] to the case of a semiprime ring.

• Bulletin of the Korean Mathematical Society
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• v.46 no.5
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• pp.857-866
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• 2009

Let n be a fixed positive integer, R be a 2n!-torsion free prime ring and $\mu$, $\nu$ be a pair of generalized derivations on R. If < $\mu^2(x)+\nu(x),\;x^n$ > = 0 for all x $\in$ R, then $\mu$ and $\nu$ are either left multipliers or right multipliers. Let n be a fixed positive integer, R be a noncommutative 2n!-torsion free prime ring with the center $C_R$ and d, g be a pair of derivations on R. If < $d^2(x)+g(x)$, $x^n$ > $\in$ $C_R$ for all x $\in$ R, then d = g = 0. Then we apply these purely algebraic techniques to obtain several range inclusion results of pair of (generalized-)derivations on a Banach algebra.

• Journal of the Chungcheong Mathematical Society
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• v.29 no.1
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• pp.37-48
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• 2016

The aim of this paper is to introduce the notion of a generalized derivations of BCH-algebras and some related properties are investigated.

• Bulletin of the Korean Mathematical Society
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• v.45 no.2
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• pp.253-261
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• 2008

In this paper, we introduce the notion of generalized left derivation on a ring R and prow that every generalized Jordan left derivation on a 2-torsion free primp ring is a generalized left derivation on R. Some related results are also obtained.

• Journal of the Chungcheong Mathematical Society
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• v.36 no.3
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• pp.163-169
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• 2023

In this article, we consider a vectorial linear connection which is determined by three fixed vector fields. Classifying these vectorial connections, we obtain a new type of generalized statistical manifolds which allow non-zero torsion.

• Honam Mathematical Journal
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• v.28 no.4
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• pp.499-511
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• 2006

It is well-known that every finitely generated torsion-free module over a principal ideal domain is free. This will be generalized. We deal with ideals of the finite, external direct product of certain rings. Finally, if M is a torsion-free, finitely generated module over a reduced, Noetherian ring A, then we prove that Ms is a projective module over As, where $S=A{\setminus}(A)$.