• 대한수학회보
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• 제60권4호
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• pp.895-903
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• 2023

In this paper, we give some results on 2-strongly Gorenstein projective modules and related rings. We first investigate the relationship between strongly Gorenstein projective modules and periodic modules and then give the structure of modules over strongly Gorenstein semisimple rings. Furthermore, we prove that a ring R is 2-strongly Gorenstein hereditary if and only if every ideal of R is Gorenstein projective and the class of 2-strongly Gorenstein projective modules is closed under extensions. Finally, we study the relationship between 2-Gorenstein projective hereditary and 2-Gorenstein projective semisimple rings, and we also give an example to show the quotient ring of a 2-Gorenstein projective hereditary ring is not necessarily 2-Gorenstein projective semisimple.

• International journal of advanced smart convergence
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• 제13권2호
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• pp.69-79
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• 2024

AI technology is a central focus of the 4th Industrial Revolution. However, compared to some existing non-artificial intelligence technologies, new AI adversarial attacks have become possible in learning data management, input data management, and other areas. These attacks, which exploit weaknesses in AI encryption technology, are not only emerging as social issues but are also expected to have a significant negative impact on existing IT and convergence industries. This paper examines various cases of AI adversarial attacks developed recently, categorizes them into five groups, and provides a foundational document for developing security guidelines to verify their safety. The findings of this study confirm AI adversarial attacks that can be applied to various types of cryptographic modules (such as hardware cryptographic modules, software cryptographic modules, firmware cryptographic modules, hybrid software cryptographic modules, hybrid firmware cryptographic modules, etc.) incorporating AI technology. The aim is to offer a foundational document for the development of standardized protocols, believed to play a crucial role in rejuvenating the information security industry in the future.

• Journal of the Optical Society of Korea
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• 제8권2호
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• pp.55-58
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• 2004

Several internal wavelength locker schemes for 10 Gbps electro-absorption modulated laser EML) module were reviewed. 10 Gbps EML modules with simple and robust internal wavelength ockers for metro dense WDM application were successfully demonstrated. The wavelength aging ver 2000 hours was done at elevated temperature of 7$0^{\circ}C$. The average wavelength drift of 10 modules was measured to be about $\pm$ 5 pm. These modules can be successfully applied to the 0 Gbps DWDM systems with 50 ㎓ channel spacing.

• Korean Journal of Mathematics
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• 제25권4호
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• pp.587-606
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• 2017

This paper is a continuation of study semi-potentness endomorphism rings of module. We give some other characterizations of endomorphism ring to be semi-potent. New results are obtained including necessary and sufficient conditions for the endomorphism ring of semi(injective) projective module to be semi-potent. Finally, we characterize a module M whose endomorphism ring it is semi-potent via direct(injective) projective modules. Several properties of the endomorphism ring of a semi(injective) projective module are obtained. Besides to that, many necessary and sufficient conditions are obtained for semi-projective, semi-injective modules to be semi-potent and co-semi-potent modules.

• Kyungpook Mathematical Journal
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• 제48권4호
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• pp.651-663
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• 2008

In this paper, we first study some characterizations of left MC2 rings. Next, by introducing left nil-injective modules, we discuss and generalize some well known results for a ring whose simple singular left modules are Y J-injective. Finally, as a byproduct of these results we are able to show that if R is a left MC2 left Goldie ring whose every simple singular left R-module is nil-injective and GJcp-injective, then R is a finite product of simple left Goldie rings.

• 충청수학회지
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• 제5권1호
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• pp.195-201
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• 1992

Let G(A) denote a generalized Kac Moody Lie algebra associated to a symmetrizable generalized Cartan matrix A. In this paper, we study on representations of G(A). Highest weight modules and the category O are described. In the main theorem we show that some G(A) modules from the category O are completely reducible. Also a criterion for irreducibility of highest weight modules is obtained. This was proved in [3] for the case of Kac Moody Lie algebras.

• Kyungpook Mathematical Journal
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• 제58권3호
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• pp.463-472
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• 2018

A Q-module is a module in which every nonzero submodule of M is a finite product of primary submodules of M. This paper is devoted to study some properties of Dedekind modules and Q-modules.

• 한국조명전기설비학회:학술대회논문집
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• 한국조명전기설비학회 2009년도 춘계학술대회 논문집
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• pp.21-23
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• 2009

The paper is to evaluate for reliability of LED Modules for Lighting by ALTs(Accelerated Life Tests). The recently, some of KS were established by law of LED Modules for Lighting(KS C 7651, KS C 7652 and KS C 7653), but reliability assessment methods of LED Modules for Lighting were not established. Therefore, the paper aided companies to test methods for accelerated life testing by themselves.

• 대한수학회보
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• 제56권6호
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• pp.1617-1642
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• 2019

In this paper, we study a theory for the structure of ${\tau}_w$-Loewy series of modules over commutative rings, where ${\tau}_w$ is the hereditary torsion theory induced by the so-called w-operation, and explore the relationship between ${\tau}_w$-Loewy modules and w-Artinian modules.

• 대한수학회논문집
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• 제36권2호
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• pp.257-266
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• 2021

In this paper, by using the sequence of adjointable operators from C^*-algebra 𝓐 into Hilbert 𝓐-module E, the woven frames of multipliers in Hilbert C^*-modules are introduced. Meanwhile, we study the effect of operators on these frames and, also we construct the new woven frame of multipliers in Hilbert 𝓐-module 𝓐. Finally, compositions of woven frames of multipliers in Hilbert C^*-modules are studied.