• 대한수학회지
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• 제54권6호
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• pp.1699-1731
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• 2017

In this note, we define and compare some closures which behave somewhat like the radical closure. Using these closures as a starting point allows us to classify all semiprime closures on the nodal curve. Several examples provided show how these closures can differ significantly in the non-Noetherian setting.

• 정보보호학회논문지
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• 제31권6호
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• pp.1137-1148
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• 2021

CSIDH 기반 암호를 구현하는 데 있어서 가장 큰 단점은 Velu 공식을 활용하여 isogeny를 연산하기 위해 작은 소수 위수를 가지는 커널의 생성점을 선택하는 부분이다. 이 과정은 작은 위수의 경우 실패확률이 크기 때문에 연산량이 많이 들어서, 최근에 radical isogeny를 사용하는 부분에 관한 연구가 진행되었다. 본 논문에서는 CSIDH기반 암호 구현에 있어서 radical isogeny를 사용하는 최적 방안에 대해 제시한다. 본 논문에서는 Montgomery 곡선과 Tate 곡선 사이의 변환을 최적하였으며, 2-, 3-, 5-, 7-isogeny에 대한 공식을 최적화하였다. 본 논문의 결과, CSIDH-512의 경우 radical isogeny를 7차까지 사용할 경우 기존 constant-time CSIDH에 비해서 15.3% 빠른 결과를 얻을 수 있었다. CSIDH-4096의 경우 radical isogeny를 2차까지 사용하는 것이 최적이라는 결론을 얻을 수 있었다.

• 대한수학회보
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• 제54권4호
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• pp.1123-1139
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• 2017

The aim in this note is to describe some classes of rings in relation to factorization by prime radical, upper nilradical, and Jacobson radical. We introduce the concepts of tpr ring, tunr ring, and tjr ring in the process, respectively. Their ring theoretical structures are investigated in relation to various sorts of factor rings and extensions. We also study the structure of noncommutative tpr (tunr, tjr) rings of minimal order, which can be a base of constructing examples of various ring structures. Various sorts of structures of known examples are studied in relation with the topics of this note.

• Kyungpook Mathematical Journal
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• 제56권2호
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• pp.397-408
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• 2016

Let R be a 2-torsion free prime ring with center Z, U be the Utumi quotient ring, Q be the Martindale quotient ring of R, d be a derivation of R and L be a Lie ideal of R. If $d(uv)^n=d(u)^md(v)^l$ or $d(uv)^n=d(v)^ld(u)^m$ for all $u,v{\in}L$, where m, n, l are xed positive integers, then $L{\subseteq}Z$. We also examine the case when R is a semiprime ring. Finally, as an application we apply our result to the continuous derivations on non-commutative Banach algebras. This result simultaneously generalizes a number of results in the literature.

• Korean Journal of Mathematics
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• 제27권1호
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• pp.141-150
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• 2019

In this article we investigate the structure of rings in which lower nilradicals coincide with upper nilradicals. Such rings shall be said to be quasi-2-primal. It is shown first that the $K{\ddot{o}}the^{\prime}s$ conjecture holds for quasi-2-primal rings. So the results in this article may provide interesting and useful information to the study of nilradicals in various situations. In the procedure we study the structure of quasi-2-primal rings, and observe various kinds of quasi-2-primal rings which do roles in ring theory.

• Kyungpook Mathematical Journal
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• 제55권4호
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• pp.871-883
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• 2015

This paper is devoted to study the divisorial submodules. We get some equivalent conditions for a submodule to be a divisorial submodule. Also we get equivalent conditions for $(N{\cap}L)^{-1}$ to be a ring, where N, L are submodules of a module M.

• 충청수학회지
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• 제31권1호
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• pp.1-12
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• 2018

Let R be a 3!-torsion free noncommutative semiprime ring, and suppose there exists a Jordan derivation $D:R{\rightarrow}R$ such that $D^2(x)[D(x),x]=0$ or $[D(x),x]D^2(x)=0$ for all $x{\in}R$. In this case we have $f(x)^5=0$ for all $x{\in}R$. Let A be a noncommutative Banach algebra. Suppose there exists a continuous linear Jordan derivation $D:A{\rightarrow}A$ such that $D^2(x)[D(x),x]{\in}rad(A)$ or $[D(x),x]D^2(x){\in}rad(A)$ for all $x{\in}A$. In this case, we show that $D(A){\subseteq}rad(A)$.

• 한국측량학회지
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• 제37권2호
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• pp.91-97
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• 2019

In automatic map generalization, the formalization of cartographic principles is important. This study proposes and evaluates the selection method for road network generalization that analyzes existing maps using reverse engineering and formalizes the selection rules for the road network. Existing maps with a 1:5,000 scale and a 1:25,000 scale are compared, and the criteria for selection of the road network data and the relative importance of each network object are determined and analyzed using $T{\ddot{o}}pfer^{\prime}s$ Radical Law as well as the logistic regression model. The selection model derived from the analysis result is applied to the test data, and road network data for the 1:25,000 scale map are generated from the digital topographic map on a 1:5,000 scale. The selected road network is compared with the existing road network data on the 1:25,000 scale for a qualitative and quantitative evaluation. The result indicates that more than 80% of road objects are matched to existing data.

• 대한수학회보
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• 제58권6호
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• pp.1401-1407
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• 2021

Let R be a commutative G-graded ring with a nonzero unity. In this article, we introduce the concept of graded radically principal ideals. A graded ideal I of R is said to be graded radically principal if Grad(I) = Grad(〈c〉) for some homogeneous c ∈ R, where Grad(I) is the graded radical of I. The graded ring R is said to be graded radically principal if every graded ideal of R is graded radically principal. We study graded radically principal rings. We prove an analogue of the Cohen theorem, in the graded case, precisely, a graded ring is graded radically principal if and only if every graded prime ideal is graded radically principal. Finally we study the graded radically principal property for the polynomial ring R[X].

• 대한수학회보
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• 제59권3호
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• pp.529-545
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• 2022

This article concerns a ring property that arises from combining one-sided duo factor rings and centers. A ring R is called right CIFD if R/I is right duo by some proper ideal I of R such that I is contained in the center of R. We first see that this property is seated between right duo and right π-duo, and not left-right symmetric. We prove, for a right CIFD ring R, that W(R) coincides with the set of all nilpotent elements of R; that R/P is a right duo domain for every minimal prime ideal P of R; that R/W(R) is strongly right bounded; and that every prime ideal of R is maximal if and only if R/W(R) is strongly regular, where W(R) is the Wedderburn radical of R. It is also proved that a ring R is commutative if and only if D₃(R) is right CIFD, where D₃(R) is the ring of 3 by 3 upper triangular matrices over R whose diagonals are equal. Furthermore, we show that the right CIFD property does not pass to polynomial rings, and that the polynomial ring over a ring R is right CIFD if and only if R/I is commutative by a proper ideal I of R contained in the center of R.