• Bulletin of the Korean Mathematical Society
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• v.18 no.2
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• pp.65-68
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• 1982

• Bulletin of the Korean Mathematical Society
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• v.58 no.1
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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.

• Bulletin of the Korean Mathematical Society
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• v.58 no.4
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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.

• Communications of the Korean Mathematical Society
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• v.37 no.2
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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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• v.18 no.2
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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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• v.30 no.1
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• pp.31-37
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• 2005

The aim of this study was to evaluate the effectiveness of sealer placement in simulated root canal extensions. Forty resin blocks were attained from the Endo-training Bloc. In each block. The simulated root canal was made with $\#20$, 80taper GT file. After each block was longitudinally split into two halves, a standardized groove was prepared on one canal wall of two halves to simulate the canal extensions with various irregularities. The two halves of each block were assembled and all simulated root canals were obturated by single cone method with AH26 sealer. Four different methods of sealer placement were used: group A, $\#20$ K-file; group B, ultrasonic file; group C, lentulo spiral; group D, EZ-Fill bi-directional spiral. All obturated blocks were stored in $100\%$ humidity at $37^{\circ}C$ for 1 week, Using a low speed saw, each block was sectioned horizontally. Images of the sections were taken using a stereomicroscope at $\times$ 30 magnification and a digital camera. The amount of the sealer in the groove was evaluated using a scoring system, a higher score indicated better sealing effectiveness. The data was statistically analysed by Fisher's Exact Test. The sealing score was the lowest, specially at the middle area of canal extensions in group A, and that was statistically significant difference from other groups. In conclusion, the ultrasonic file, lentulo spiral and EZ-Fill bi-directional spiral were effective methods of sealer placement in simulated canal extensions. The K file was the least effective method, specially at the middle area of canal extensions.

• The Pure and Applied Mathematics
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• v.23 no.1
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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.

• Bulletin of the Korean Mathematical Society
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• v.58 no.1
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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.

• Communications of the Korean Mathematical Society
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• v.30 no.3
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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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• v.21 no.4
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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.