• 대한수학회보
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• 제18권2호
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• pp.65-68
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• 1982

• 대한수학회보
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• 제58권1호
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• pp.183-193
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• 2021

In this paper, we prove that there is a bijection between the ��-tilting modules and the sincere left finite semibricks. We also construct (sincere) semibricks over split-by-nilpotent extensions. More precisely, let �� be a split-by-nilpotent extension of a finite-dimensional algebra �� by a nilpotent bimodule ��E��, and �� ⊆ mod ��. We prove that �� ⊗�� �� is a (sincere) semibrick in mod �� if and only if �� is a semibrick in mod �� and Hom��(��, �� ⊗�� E) = 0 (and �� ∪ �� ⊗�� E is sincere). As an application, we can construct ��-tilting modules and support ��-tilting modules over ��-tilting finite cluster-tilted algebras.

• 대한수학회보
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• 제58권4호
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• pp.865-876
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• 2021

Let 𝔽 be a commutative ring. A restricted skew polynomial extension over 𝔽 is a class of iterated skew polynomial 𝔽-algebras which include well-known quantized algebras such as the quantum algebra U_q(𝔰𝔩₂), Weyl algebra, etc. Here we obtain a necessary and sufficient condition in order to be restricted skew polynomial extensions over 𝔽. We also introduce a restricted Poisson polynomial extension which is a class of iterated Poisson polynomial algebras and observe that a restricted Poisson polynomial extension appears as semiclassical limits of restricted skew polynomial extensions. Moreover, we obtain usual as well as unusual quantized algebras of the same Poisson algebra as applications.

• 대한수학회논문집
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• 제37권2호
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• pp.327-335
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• 2022

Let R be a commutative ring with identity. We call the ring R to be an almost weakly finite conductor if for any two elements a and b in R, there exists a positive integer n such that aⁿR ∩ bⁿR is finitely generated. In this article, we give some conditions for the trivial ring extensions and the amalgamated algebras to be almost weakly finite conductor rings. We investigate the transfer of these properties to trivial ring extensions and amalgamation of rings. Our results generate examples which enrich the current literature with new families of examples of nonfinite conductor weakly finite conductor rings.

• Korean Journal of Mathematics
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• 제18권2호
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• pp.119-132
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• 2010

P. M. Cohn called a ring R reversible if whenever ab = 0, then ba = 0 for $a,b{\in}R$. In this paper, we study an extension of a reversible ring with its endomorphism. An endomorphism ${\alpha}$ of a ring R is called strong right (resp., left) reversible if whenever $a{\alpha}(b)=0$ (resp., ${\alpha}(a)b=0$) for $a,b{\in}R$, ba = 0. A ring R is called strong right (resp., left) ${\alpha}$-reversible if there exists a strong right (resp., left) reversible endomorphism ${\alpha}$ of R, and the ring R is called strong ${\alpha}$-reversible if R is both strong left and right ${\alpha}$-reversible. We investigate characterizations of strong ${\alpha}$-reversible rings and their related properties including extensions. In particular, we show that every semiprime and strong ${\alpha}$-reversible ring is ${\alpha}$-rigid and that for an ${\alpha}$-skew Armendariz ring R, the ring R is reversible and strong ${\alpha}$-reversible if and only if the skew polynomial ring $R[x;{\alpha}]$ of R is reversible.

• Restorative Dentistry and Endodontics
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• 제30권1호
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• pp.31-37
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• 2005

본 실험은 resin 시편을 이용하여 미리 제작한 근관 내 불규칙 확장부에서 근관 충전용 sealer의 적용 방법에 따른 충전 효과를 평가해 보았다. Endo-training Bloc을 절단하여 사십 개의 규격화된 resin 블록 시편을 획득하였다. 각각의 시편에 $\#20$, 08taper GT 파일을 사용하여 근관을 형성하였고 근관에 손상이 가지 않도록 시편을 양분한 후 양분된 시편의 한 쪽 근관 벽에 다양한 근관 내 확장부를 표현하는 구를 형성하였다. 양분된 시편을 결찰하고 절단 부위를 밀봉하였으며 AH26 sealer를 사용하여 단일 cone 충전법으로 근관을 충전하였다. 네 가지의 근관 충전용 sealer의 적용방법을 이용하였다: A군, $\#20$ K-file : B군, ultrasonic file : C군, lentulo spiral: D군. EZ-Fill bi-directioanl spiral. 모든 시편은 $37^{\circ}\;100\%$ 상대습도에서 1주일간 보관한 후 각 시편을 근단에서 3mm, 4mm, 5mm 부위에서 수평으로 절단하고 각각의 절단면을 위상차현미경과 디지털 카메라를 이용하여 30배율로 관찰하고 촬영하였다. 관찰된 절단면은 scoring system을 이용하여 점수를 산정하였고 각 군 간의 통계적인 유의성 유무는 Fisher's Exact Test를 이용하여 시행하였다.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제23권1호
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• pp.53-59
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• 2016

Let G be a finite group containing a non-abelian Sylow 2-subgroup. We elementarily show that every G-Galois field extension L/K has a hyperbolic trace form in the presence of root of unity.

• 대한수학회보
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• 제58권1호
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• pp.47-58
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• 2021

In this article, we completely determine the rings for which every element is a sum of a nilpotent and three tripotents that commute with one another. We discuss this property for some extensions of rings, including group rings.

• 대한수학회논문집
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• 제30권3호
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• pp.239-252
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• 2015

Motivated mainly by certain interesting extensions of the ${\tau}$-hypergeometric function defined by Virchenko et al. [11] and some ${\tau}$-Appell's function introduced by Al-Shammery and Kalla [1], we introduce here the ${\tau}$-Lauricella functions $F_A^{(n),{\tau}_1,{\cdots},{\tau}_n}$, $F_B^{(n),{\tau}_1,{\cdots},{\tau}_n}$ and $F_D^{(n),{\tau}_1,{\cdots},{\tau}_n}$ and the confluent forms ${\Phi}_2^{(n),{\tau}_1,{\cdots},{\tau}_n}$ and ${\Phi}_D^{(n),{\tau}_1,{\cdots},{\tau}_n}$ of n variables. We then systematically investigate their various integral representations of each of these ${\tau}$-Lauricella functions including their generating functions. Various (known or new) special cases and consequences of the results presented here are also considered.

• ALGAE
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• 제21권4호
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• pp.445-452
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• 2006

The morphometry and distribution of the unarmoured dinoflagellates Brachidinium capitatum F.J.R. Taylor, Asterodinium gracile Sournia, Microceratium orstomii Sournia and the toxic species Karenia papilionacea Haywood et Steidinger have been investigated in open waters of the SE Pacific Ocean. The genus Microceratium Sournia is recorded for the first time since the initial description. These taxa showed a high morphological similarity and they may correspond to life stages of a highly versatile single species that is able to project body extensions. Karenia papilionacea showed the higher abundance in the surface waters of the more productive areas (the Marquesas Archipelago and the Perú-Chile Current). Brachidinium capitatum and K. papilionacea often co-occurred, predominating B. capitatum in offshore surface waters. Asterodinium gracile was recorded at the bottom of the euphotic zone (down to 210 m depth), with a shallower distribution in more productive areas. Intermediate specimens of Asterodinium-Brachidinium-Karenia, with variable disposition and size of the body extensions were illustrated.