• Bulletin of the Korean Mathematical Society
• /
• v.58 no.5
• /
• pp.1221-1233
• /
• 2021

In this paper, we introduce and investigate a new class of modules that is closely related to the class of Noetherian modules. Let R be a commutative ring and M be an R-module. We say that M is an r-Noetherian module if every r-submodule of M is finitely generated. Also, we call the ring R to be an r-Noetherian ring if R is an r-Noetherian R-module, or equivalently, every r-ideal of R is finitely generated. We show that many properties of Noetherian modules are also true for r-Noetherian modules. Moreover, we extend the concept of weakly Noetherian rings to the category of modules and we characterize Noetherian modules in terms of r-Noetherian and weakly Noetherian modules. Finally, we use the idealization construction to give non-trivial examples of r-Noetherian rings that are not Noetherian.

• Bulletin of the Korean Mathematical Society
• /
• v.59 no.2
• /
• pp.453-468
• /
• 2022

In this article, we define a module M to be G^z-extending if and only if for each z-closed submodule X of M there exists a direct summand D of M such that X ∩ D is essential in both X and D. We investigate structural properties of G^z-extending modules and locate the implications between the other extending properties. We deal with decomposition theory as well as ring and module extensions for G^z-extending modules. We obtain that if a ring is right G^z-extending, then so is its essential overring. Also it is shown that the G^z-extending property is inherited by its rational hull. Furthermore it is provided some applications including matrix rings over a right G^z-extending ring.

• Communications of the Korean Mathematical Society
• /
• v.35 no.2
• /
• pp.469-480
• /
• 2020

Let R be a commutative ring with identity and M a unital R-module. We give a new generalization of exact sequences called e-exact sequences. A sequence $0{\rightarrow}A{\longrightarrow[20]^f}B{\longrightarrow[20]^g}C{\rightarrow}0$ is said to be e-exact if f is monic, Imf ≤_e Kerg and Img ≤_e C. We modify many famous theorems including exact sequences to one includes e-exact sequences like 3 × 3 lemma, four and five lemmas. Next, we prove that for torsion-free module M, the contravariant functor Hom(-, M) is left e-exact and the covariant functor M ⊗ - is right e-exact. Finally, we define e-projective module and characterize it. We show that the direct sum of R-modules is e-projective module if and only if each summand is e-projective.

• Journal of Power Electronics
• /
• v.14 no.6
• /
• pp.1189-1196
• /
• 2014

A modular multilevel-clamped composited multilevel converter ($M-MC^2$) is proposed. $M-MC^2$ enables topology reconfiguration, power device reuse, and composited clamping. An advanced five-level converter ($5L-M-MC^2$) is derived from the concept of $M-MC^2$. $5L-M-MC^2$ integrates dual three-level T-type modules and one three-level neutral point clamped module. This converter can also integrate dual three-level T-type modules and one passive diode module by utilizing the device reuse scheme. The operation principle and SPWM modulation are discussed to highlight converter performance. The proposed $M-MC^2$ is comprehensively compared with state-of-the-art five-level converters. Finally, simulations and experimental results are presented to validate the effectiveness of the main contributions of this study.

• Kyungpook Mathematical Journal
• /
• v.64 no.1
• /
• pp.1-14
• /
• 2024

Recently, Zhao, Wang, and Pu introduced and studied new concepts of nonnil-commutative diagrams and nonnil-projective modules. They proved that an R-module that is nonnil-isomorphic to a projective module is nonnil-projective, and they proposed the following problem: Is every nonnil-projective module nonnil-isomorphic to some projective module? In this paper, we delve into some new properties of nonnil-commutative diagrams and answer this problem in the affirmative.

• Kyungpook Mathematical Journal
• /
• v.49 no.3
• /
• pp.557-562
• /
• 2009

A module M is said to be SIP-extending if the intersection of every pair of direct summands is essential in a direct summand of M. SIP-extending modules are a proper generalization of both SIP-modules and extending modules. Every direct summand of an SIP-module is an SIP-module just as a direct summand of an extending module is extending. While it is known that a direct sum of SIP-extending modules is not necessarily SIP-extending, the question about direct summands of an SIP-extending module to be SIP-extending remains open. In this study, we show that a direct summand of an SIP-extending module inherits this property under some conditions. Some related results are included about $C_{11}$ and SIP-modules.

• Proceedings of the Korean Information Science Society Conference
• /
• 2002.10c
• /
• pp.541-543
• /
• 2002

정보기술의 발전은 디지털 혁명의 근간이 되고 있는 반면, 정보유출ㆍ파괴ㆍ변조 등의 역기능 또한 내포하기 때문에 이러한 정보화의 역기능에 대한 신속한 탐지 및 능동적인 대응이 절실히 요구되고 있는 실정이다. 그러나 기존의 시스템은 침입에 대한 차단을 중심으로 운영되어 왔고, 침입탐지 시스템이라 할지라도 불법 침입에 대한 대응이 단지 경고나 보고 수준에 머물고 있어 능동적인 대응이 없다는 단점이 있다. 따라서 본 논문에서는 리눅스 시스템에서 실시간 침입탐지 시스템인 NIDS를 설계 구현하고, 동일 네트워크 망에서의 여러 호스트들을 통합적으로 관리하기 위하여 M/A 시스템을 설계ㆍ구현하였다. 여기서 NIDS와 M/A 시스템간의 통신은 SSL/TLS 프로토콜을 기반으로 이루어진다. NIDS에서는 Detection Module과 Response Module을 분리하여 구현하였고, 커널 레벨에서 PCAP 라이브러리를 통해 캡쳐된 패킷이 Detection Module에 의해 침입이라 판단되면 Response Module에서 일정 수준의 대응이 가능하도록 구현하였다.

• Journal of Environmental Science International
• /
• v.9 no.2
• /
• pp.173-176
• /
• 2000

This study was carried out to investigate the filtration characteristics of membrane modules according to hollow fiber dispersion for direct solid-liquid separation of activated sludge. 2 bundle, 4 bundle, and 10 bundle, and 10 bundle module used in this experiment according to hollow fiber dispersion was manufactured at laboratory and permeate flux and transmembrane pressure(TMP) of each module were observed under a suction pressure of 0.5kgf/c$m^2$. As the hollow fibers were dispersed, permeate flux was increased and TMP was decreased. Permeate flux and TMP of each module was 15.0 $\ell$/$m^2$.h and 31.8 cmHg for 2 bundle, 16.0 $\ell$/$m^2$ .h and 17.4 cmHg for 4 bundle, and 20.4 $\ell$/m2 .h and 31.8 cmHg for 10 bundle. In conclusion, the membrane fouling is expected to be decrease by maintaining lower TMP with hollow fiber dispersion.

• Bulletin of the Korean Mathematical Society
• /
• v.57 no.3
• /
• pp.763-780
• /
• 2020

Let R be a commutative ring. An R-module M is said to be w-flat if Tor ^R₁ (M, N) is GV -torsion for any R-module N. It is known that every flat module is w-flat, but the converse is not true in general. The w-flat dimension of a module is defined in terms of w-flat resolutions. In this paper, we study the w-flat dimension of an injective w-module. To do so, we introduce and study the so-called w-copure (resp., strongly w-copure) flat modules and the w-copure flat dimensions for modules and rings. The relations between the introduced dimensions and other (classical) homological dimensions are discussed. We also study change of rings theorems for the w-copure flat dimension in various contexts. Finally some illustrative examples regarding the introduced concepts are given.

• Journal of The Korea Institute of Healthcare Architecture
• /
• v.27 no.3
• /
• pp.71-78
• /
• 2021

Purpose: It is important to plan the ward module at a time when the size of beds, the floor area, and the construction budget are all set prior to the hospital design. In this context this study aims (1) to derive various factors affecting the ward module, and (2) to analyze the appropriate room module according to the type. Methods: Design factors related to hospital modules are derived through precedential studies, and the types of ward elevation are classified by reviewing the drawings of 18 case hospitals. And the detailed dimensions and area of the derived elements are analyzed. Results: The X-axis modules of the ward are switched to long span structural columns of 9.9 m, 12.6 m and 13.2 m, but the ward modules still represent 6.6 m. The Y-axis module of the ward shows a dimension of 9 to 9.9m in the process of changing a multi-person room into a four-person room. Type A of curtain wall with columns located on the wall of the room and type B of curtain wall located in the center of the room are analyzed due to their variations. The square window type, which forms the elevation of the square window by exposing the columns to the elevation, and the outframe type, which protrudes from the structural columns and beams, have elevation designs limited. There are, however, no obstacles to the interior space of the hospital room, so the wall composition and furniture arrangement are expected to be free. The ward area of Curtain Wall Type A, which can secure an effective area of 5.9m*5.0m, are 52.1m². The Curtain Wall Type A, Square window type, and the outframe type are 49.8m². Implications: As part of the hospital standard module plan for economical and reasonable hospital building planning, a type was proposed in this study in conjunction with the external design. It is hoped that it be a base for standard module research linked together to the Central Treatment department, Outpatient department and underground parking lot.