• 대한수학회지
• /
• 제44권3호
• /
• pp.719-731
• /
• 2007

R is called a right ${\Pi}-coherent$ ring in case every finitely generated torsion less right R-module is finitely presented. In this paper, we define a dimension for rings, called ${\Pi}-coherent$ dimension, which measures how far away a ring is from being ${\Pi}-coherent$. This dimension has nice properties when the ring in question is coherent. In addition, we study some properties of ${\Pi}-coherent$ rings in terms of preenvelopes and precovers.

• 대한수학회보
• /
• 제51권2호
• /
• pp.579-594
• /
• 2014

Let R be a ring and $Nil_*$(R) be the prime radical of R. In this paper, we say that a ring R is left $Nil_*$-coherent if $Nil_*$(R) is coherent as a left R-module. The concept is introduced as the generalization of left J-coherent rings and semiprime rings. Some properties of $Nil_*$-coherent rings are also studied in terms of N-injective modules and N-flat modules.

• 대한수학회보
• /
• 제47권3호
• /
• pp.611-622
• /
• 2010

A ring R is called left max-coherent provided that every maximal left ideal is finitely presented. $\mathfrak{M}\mathfrak{I}$ (resp. $\mathfrak{M}\mathfrak{F}$) denotes the class of all max-injective left R-modules (resp. all max-flat right R-modules). We prove, in this article, that over a left max-coherent ring every right R-module has an $\mathfrak{M}\mathfrak{F}$-preenvelope, and every left R-module has an $\mathfrak{M}\mathfrak{I}$-cover. Furthermore, it is shown that a ring R is left max-injective if and only if any left R-module has an epic $\mathfrak{M}\mathfrak{I}$-cover if and only if any right R-module has a monic $\mathfrak{M}\mathfrak{F}$-preenvelope. We also give several equivalent characterizations of MI-injectivity and MI-flatness. Finally, $\mathfrak{M}\mathfrak{I}$-dimensions of modules and rings are studied in terms of max-injective modules with the left derived functors of Hom.

• 대한수학회지
• /
• 제46권1호
• /
• pp.99-111
• /
• 2009

A ring is called left P-coherent if every principal left ideal is finitely presented. Let M be a right R-module with the endomorphism ring S. We mainly study the P-coherence of S. It is shown that S is a left P-coherent ring if and only if the left annihilator $ann_S$(X) is a finitely generated left ideal of S for any M-cyclic submodule X of M if and only if every cyclically M-presented right R-module has an M-torsionfree preenvelope. As applications, we investigate when the endomorphism ring S is left PP or von Neumann regular.

• 대한수학회논문집
• /
• 제39권3호
• /
• pp.623-642
• /
• 2024

This paper introduces and studies a generalization of (n, d)-rings introduced and studied by Costa in 1994 to rings with prime nilradical. Among other things, we establish that the ϕ-von Neumann regular rings are exactly either ϕ-(0, 0) or ϕ-(1, 0) rings and that the ϕ-Prüfer rings which are strongly ϕ-rings are the ϕ-(1, 1) rings. We then introduce a new class of rings generalizing the class of n-coherent rings to characterize the nonnil-coherent rings introduced and studied by Bacem and Benhissi.

• 대한수학회논문집
• /
• 제39권1호
• /
• pp.45-58
• /
• 2024

Let R be a commutative ring with identity. If the nilpotent radical N il(R) of R is a divided prime ideal, then R is called a ϕ-ring. Let R be a ϕ-ring and S be a multiplicative subset of R. In this paper, we introduce and study the class of nonnil-S-coherent rings, i.e., the rings in which all finitely generated nonnil ideals are S-finitely presented. Also, we define the concept of ϕ-S-coherent rings. Among other results, we investigate the S-version of Chase's result and Chase Theorem characterization of nonnil-coherent rings. We next study the possible transfer of the nonnil-S-coherent ring property in the amalgamated algebra along an ideal and the trivial ring extension.

• 대한수학회논문집
• /
• 제38권3호
• /
• pp.705-714
• /
• 2023

Bennis and El Hajoui have defined a (commutative unital) ring R to be S-coherent if each finitely generated ideal of R is a S-finitely presented R-module. Any coherent ring is an S-coherent ring. Several examples of S-coherent rings that are not coherent rings are obtained as byproducts of our study of the transfer of the S-coherent property to trivial ring extensions and amalgamated duplications.

• Journal of the Optical Society of Korea
• /
• 제17권1호
• /
• pp.57-62
• /
• 2013

We have numerically implemented a receiver side all-optical signal processing method, i.e. optical backward propagation (OBP), by dispersion compensating fiber (DCF) and non-linear compensator (NLC) devised by effective negative Kerr non-linear coefficient using two highly non-linear fibers (HNLFs). The method is implemented for the post-processing of fiber transmission impairments, i.e. chromatic dispersion (CD) and non-linearities (NL). The OBP module is evaluated for dual-polarization (DP) m-ary (m=4,16,32,64,256) quadrature amplitude modulation (QAM) in 112 Gbit/s coherent transmission over 1200 km standard single mode fiber (SMF). We have also investigated an intensity limited optical backward propagation module (IL-OBP) by using a self-phase modulation-based optical limiter with an appropriate pre-chirping to compensate for the intensity fluctuations in the transmission link. Our results show that in highly non-linear sensitive 256QAM transmission, we have observed a 66% increase in the transmission distance by implementing IL-OBP as compared to conventional OBP.

• Journal of the Optical Society of Korea
• /
• 제14권4호
• /
• pp.431-437
• /
• 2010

A stack of gradient-index (GRIN) rod lenses cannot be used for coherent anti-Stokes Raman scattering (CARS) microendoscopy for insertion to internal organs through a surgical keyhole with minimal invasiveness. That's because GRIN lens has large amount of inherent chromatic aberrations in spite of absolutely requiring a common focus for pump and Stokes beam with each frequency of ${\omega}_p$ and ${\omega}_S$. For this endoscopic purpose, we need to develop a long slender probe-type objective, namely probe-type microscope objective (PMO). In this paper, we introduce the structure, the working principle, and the design techniques of PMO which is composed of a probe-type lens module (PLM) and an adaptor lens module (ALM). PLM is first designed for a long slender type and ALM is successively designed by using several design parameters from PLM for eliminating optical discords between scanning unit and PLM. A combined module is optimized again to eliminate some coupling disparities between PLM and ALM for the best PMO. As a result, we can obtain a long slender PMO with perfectly diffraction-limited performance for pump beam of 817 nm and Stokes beam of 1064 nm.

• 한국정보과학회논문지:시스템및이론
• /
• 제31권12호
• /
• pp.716-725
• /
• 2004

고성능 PC 클러스터 시스템을 구축하기 위해서는 네트워크 접근 시간을 최소화하는 것이 중요하다. SCI 기반 PC 클러스터 시스템에서는 각 노드에 네트워크 캐쉬를 유지함으로써 네트워크 접근 시간을 줄이는 것이 가능하다. 본 논문에서는 공유 메모리를 PCI 버스상에 위치시킴으로써 네트워크 캐쉬지원을 가능하게 하였으며, 이에 기반한 Network Cache Coherenet NUMA(NCC-NUMA) 시스템을 제안하고, 핵심 모듈인 NCC-NUMA 카드를 개발하였다. NCC-NUMA 카드는 각 노드의 PCI 슬롯(slot)에 plug-in되는 형태이며, 공유메모리, 네트워크 캐쉬, 공유메모리 제어 모듈 및 네트워크 제어 모듈을 포함한다. 공유메모리와 네트워크 캐쉬 사이의 일관성은 IEEE SCI 표준에 의해 유지된다. NCC-NUMA 시스템의 성능 측정을 위해 SPLASH-2 벤치마크를 수행하였으며, NCC-NUMA 시스템이 네트워크 캐쉬를 활용하지 않는 NUMA 기반 클러스터 시스템에 비해서 최대 56%의 성능향상을 보임을 알 수 있었다.