• East Asian mathematical journal
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• 제37권1호
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• pp.33-40
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• 2021

We discuss the condition that if ab = 0 for elements a, b in a ring R then aIb = 0 for some essential ideal I of R. A ring with such condition is called IEIP. We prove that a ring R is IEIP if and only if Dn(R) is IEIP for every n ≥ 2, where Dn(R) is the ring of n by n upper triangular matrices over R whose diagonals are equal. We construct an IEIP ring that is not Abelian and show that a well-known Abelian ring is not IEIP, noting that rings with the insertion-of-factors-property are Abelian.

• Kyungpook Mathematical Journal
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• 제62권4호
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• pp.641-655
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• 2022

A right R-module N is called pseudo semisimple-M-injective if for any monomorphism from every semisimple submodule of M to N, can be extended to a homomorphism from M to N. In this paper, we study some properties of pseudo semisimple-injective modules. Moreover, some results of pseudo semisimple-injective modules over formal triangular matrix rings are obtained.

• 대한수학회논문집
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• 제36권1호
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• pp.27-39
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• 2021

We discuss the condition that every nonzero right annihilator of an element contains a nonzero ideal, as a generalization of the insertion-of-factors-property. A ring with such condition is called right AP. We prove that a ring R is right AP if and only if Dn(R) is right AP for every n ≥ 2, where Dn(R) is the ring of n by n upper triangular matrices over R whose diagonals are equal. Properties of right AP rings are investigated in relation to nilradicals, prime factor rings and minimal order.

• 대한수학회보
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• 제38권4호
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• pp.727-733
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• 2001

Let A be a commutative ring with nonzero identity and let M be an A-module. In this note we show that if $x = x_1, ..., x_n\; and\; y = y_1, ..., y_n$ both M-cosequence such that $Hx^T = y^T\; for\; some\; n\times n$ lower triangular matrix H over A, then the map $\beta_H : \;Ann_M(y_1,..., y_n)\;\rightarrow Ann_M(x_1,..., x_n)$ induced by multiplication by ｜H｜ is surjective.

• 대한수학회지
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• 제47권3호
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• pp.455-466
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• 2010

For an endomorphism $\alpha$ of a ring R, we introduce the weak $\alpha$-skew Armendariz rings which are a generalization of the $\alpha$-skew Armendariz rings and the weak Armendariz rings, and investigate their properties. Moreover, we prove that a ring R is weak $\alpha$-skew Armendariz if and only if for any n, the $n\;{\times}\;n$ upper triangular matrix ring $T_n(R)$ is weak $\bar{\alpha}$-skew Armendariz, where $\bar{\alpha}\;:\;T_n(R)\;{\rightarrow}\;T_n(R)$ is an extension of $\alpha$ If R is reversible and $\alpha$ satisfies the condition that ab = 0 implies $a{\alpha}(b)=0$ for any a, b $\in$ R, then the ring R[x]/($x^n$) is weak $\bar{\alpha}$-skew Armendariz, where ($x^n$) is an ideal generated by $x^n$, n is a positive integer and $\bar{\alpha}\;:\;R[x]/(x^n)\;{\rightarrow}\;R[x]/(x^n)$ is an extension of $\alpha$. If $\alpha$ also satisfies the condition that ${\alpha}^t\;=\;1$ for some positive integer t, the ring R[x] (resp, R[x; $\alpha$) is weak $\bar{\alpha}$-skew (resp, weak) Armendariz, where $\bar{\alpha}\;:\;R[x]\;{\rightarrow}\;R[x]$ is an extension of $\alpha$.

• 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.

• 한국정밀공학회:학술대회논문집
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• 한국정밀공학회 2003년도 춘계학술대회 논문집
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• pp.533-537
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• 2003

Compared to sintered polycrystalline diamond (PCD), the deposited thin film diamond has a great advantage on the fabrication of cutting tools with complex geometries such as drills. Because of high performance in high speed machining non-ferrous difficult-to-cut materials in the field of automobiles industry, aeronautics and astronautics industry, diamond-coated drills find large potentialities in commercial applications. However, the poor adhesion of the diamond film on the substrate and high surface roughness of the drill flute adversely affect the tool lift and machining quality and they become the main technical barriers for the successful development and commercialization of diamond-coated drills. In this paper, diamond thin films were deposited on the commercial WC-Co based drills by the electron aided hot filament chemical vapor deposition (EACVD). A new multiple coating technology based on changing gas pressure in different process stages was developed. The large triangular faceted diamond grains may have great contribution to the adhesive strength between the film and the substrate, and the overlapping ball like blocks consisted of nanometer sized diamond crystals may contribute much to the very low roughness of diamond film. Adhesive strength and quality of diamond film were evaluated by scanning electron microscope (SEM), atomic force microscope (AFM), Raman spectrum and drilling experiments. The ring-block tribological experiments were also conducted and the results revealed that the friction coefficient increased with the surface roughness of the diamond film. From a practical viewpoint, the cutting performances of diamond-coated drills were studied by drilling the SiC particles reinforced aluminum-matrix composite. The good adhesive strength and low surface roughness of flute were proved to be beneficial to the good chip evacuation and the decrease of thrust and consequently led to a prolonged tool lift and an improved machining quality. The wear mechanism of diamond-coated drills is the abrasive mechanical attrition.

• 한국결정학회지
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• 제15권2호
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• pp.59-68
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• 2004

부분적으로 $Co^{2+}$ 이온으로 치환된 제올라이트 A를 진공 탈수한 후 $300^{\circ}C$에서 12시간, 6시간, 2시간 동안 각각 0.6 torr의 K증기로 반응시킨 3개의 구조$(a=12.181(1)\;{\AA},\; a=12.184(1)\;{\AA},\; a=12.215(1)\;{\AA})$를 $21^{\circ}C$에서 입방공간군 Pm3m를 사용하여 단결정 X-선 회절법으로 해석하고 정밀화한다. K 증기로 반응시킨 3개의 구조는 Full-matrix 최소자승법 정밀화 계산에서 $1>\sigma(I)$인 70, 82, 80개의 독립반사를 각각 사용하여 최종오차인자를 R (weight) = 0.090, 0.091, 0.090까지 각각 정밀화한다. 3개의 구조에서 4개의$Co^{2+}$이온과 4개의 $Na^+$이온모두 K증기에 의해서 환원되어 $Co^{2+}$ 이온과 $Na^+$ 이온은 제올라이트 내에 더 이상 생성되지 않는다. K종류는 5개의 다른 결정학적 자리에 위치하는데 3개의 $K^+$이온은 8-링의 평면에 완전히 채워져 위치하고 약 11.5개의 $K^+$ 이온은 3회 회전축상의 6-링에 위치하고 약 4개는 큰 동공, 4개는 소다라이트 동공, 0.5개는 큰 공동의 4-링과 마주보는 위치에 위치하고 3개의 $K^0$원자는 3회 회전축상의 큰 동공 깊숙이 위치한다. 이들 구조는 제올라이트 A의 소다라이트 동공에서 사면체 $K_4$ (혹은 삼각형 $K_3$) 클라스터를 이루고 있으며 $K_4$ 혹은 $K_3$ 클라스터는 6-링의 3개의 산소와 삼면체로 결합한다. 이들 클라스터의 부분적으로 환원된 이온은 제올라이트 골조 산소와 우선적으로 결합한다. 이들 구조에서 제올라이트 골조의 음전하를 상쇄시키는데 필요한 12개의 $K^+$ 이온보다 많은 단위세포당 14.5개의 K종류가 존재하는데 이들 결과로 $K^0$원자가 흡착되었음을 알 수 있다. 큰 동공 깊숙이 위치한 3개의 $K^0$ 원자는 4개의 큰 동공에 위치한 $K^+$ 이온 중 3개와 결합하여 $K_7^{4+}$클라스터를 형성하며$K_7^{4+}$ 클라스터는 골조산소와 우선적으로 결합한다.