• Honam Mathematical Journal
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• v.23 no.1
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• pp.15-20
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• 2001

Reduced Von Neumann Regular ring is pseudo symmetric and N(R) is reduced. Thus N(R) is pseudo symmetric and M(R) is reduced if and only if M(R) = N(R).

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2007.11a
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• pp.77-78
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• 2007

• Bulletin of the Korean Mathematical Society
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• v.56 no.3
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• pp.659-666
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• 2019

In this paper, we consider a conjecture of I. N. Herstein for local commutators of symmetric elements and unitary elements of division rings. For example, we show that if D is a finite dimensional division ring with involution ${\star}$ and if $a{\in}D^*=D{\setminus}\{0\}$ such that local commutators $axa^{-1}x^{-1}$ at a are radical over the center F of D for every $x{\in}D^*$ with $x^{\star}=x$, then either $a{\in}F$ or ${\dim}_F\;D=4$.

• Communications of the Korean Mathematical Society
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• v.28 no.4
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• pp.669-677
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• 2013

In this paper we introduce the notion of NI near-rings similar to the notion introduced in rings. We give topological properties of collection of strongly prime ideals in NI near-rings. We have shown that if N is a NI and weakly pm near-ring, then $Max(N)$ is a compact Hausdorff space. We have also shown that if N is a NI near-ring, then for every $a{\in}N$, $cl(D(a))=V(N^*(N)_a)=Supp(a)=SSpec(N){\setminus}int\;V(a)$.

• The Mathematical Education
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• v.49 no.4
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• pp.489-500
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• 2010

This study makes clear justification of contents of set in secondary school through the scientific consideration and contents consideration of curriculum about two points - lattice and ring - of set deal with 'number and operation'. In this process, we make clear the greatest common divisor, the least common multiple and operation of set, especially the meaning of symmetric difference, we suggest direction about constitution of contents of set in secondary school. This study helps to raise the specificity on the elements of textbook and presents the first step about the range of teaching in a construct of curriculum.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2007.11a
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• pp.1218-1223
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• 2007

In this study, we experimentally investigate the equivalent ring theory for a slightly asymmetric ring. The slightly asymmetric ring has mode pair and frequency pair due to the small asymmetry and this mode pair generates beat in vibration and sound. In this paper, a slightly asymmetric ring is modeled as the equivalent ring, i.e., the assemblage of a symmetric ring and imperfect point masses. The equivalent ring has the same mode pair condition as that of the original asymmetric ring. Effect of the additional mass attachment is investigated by the equivalent ring theory and the result is compared with those of the measurement and the finite element analysis. It is confirmed that the original ring and the equivalent ring show the same change in frequency and mode under the various additional imperfection mass conditions. The equivalent ring theory explains how the asymmetric elements influence the mode characteristics and provides useful information to tune the beat property.

• Kyungpook Mathematical Journal
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• v.51 no.3
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• pp.301-309
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• 2011

In this paper we dene the notions of left *-bimultiplier, *-bimultiplier and generalized *-biderivation, and to prove that if a semiprime *-ring admits a left *-bimultiplier M, then M maps R ${\times}$ R into Z(R). In Section 3, we discuss the applications of theory of *-bimultipliers. Further, it was shown that if a semiprime *-ring R admits a symmetric generalized *-biderivation G : R ${\times}$ R ${\rightarrow}$ R with an associated nonzero symmetric *-biderivation R ${\times}$ R ${\rightarrow}$ R, then G maps R ${\times}$ R into Z(R). As an application, we establish corresponding results in the setting of $C^*$-algebra.

• Kyungpook Mathematical Journal
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• v.61 no.1
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• pp.11-21
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• 2021

We study the structure of rings whose factor rings modulo nonzero proper ideals are right duo; such rings are called right FD. We first see that this new ring property is not left-right symmetric. We prove for a non-prime right FD ring R that R is a subdirect product of subdirectly irreducible right FD rings; and that R/N∗(R) is a subdirect product of right duo domains, and R/J(R) is a subdirect product of division rings, where N∗(R) (J(R)) is the prime (Jacobson) radical of R. We study the relation among right FD rings, division rings, commutative rings, right duo rings and simple rings, in relation to matrix rings, polynomial rings and direct products. We prove that if a ring R is right FD and 0 ≠ e2 = e ∈ R then eRe is also right FD, examining that the class of right FD rings is not closed under subrings.

• Kyungpook Mathematical Journal
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• v.46 no.2
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• pp.153-167
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• 2006

We study permuting tri-derivations in ${\Gamma}$-rings and give an example.

• Communications of the Korean Mathematical Society
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• v.15 no.3
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• pp.469-479
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• 2000

We define and study the extended centroid of a prime $\Gamma$-ring.