• Journal of the Korean Mathematical Society
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• v.44 no.3
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• pp.719-731
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• 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.

• Bulletin of the Korean Mathematical Society
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• v.51 no.2
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• pp.579-594
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• 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.

• Bulletin of the Korean Mathematical Society
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• v.47 no.3
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• pp.611-622
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• 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.

• Journal of the Korean Mathematical Society
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• v.46 no.1
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• pp.99-111
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• 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.

• Communications of the Korean Mathematical Society
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• v.39 no.3
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• pp.623-642
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• 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.

• Communications of the Korean Mathematical Society
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• v.39 no.1
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• pp.45-58
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• 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.

• Communications of the Korean Mathematical Society
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• v.38 no.3
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• pp.705-714
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• 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
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• v.17 no.1
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• pp.57-62
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• 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
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• v.14 no.4
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• pp.431-437
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• 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.

• Journal of KIISE:Computer Systems and Theory
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• v.31 no.12
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• pp.716-725
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• 2004

It is extremely important to minimize network access time in constructing a high-performance PC cluster system. For PC cluster systems, it is possible to reduce network access time by maintaining network cache in each cluster node. This paper presents a Network Cache Coherent NUMA (NCC-NUMA) system to utilize network cache by locating shared memory on the PCI bus, and the NCC-NUMA card which is core module of the NCC-NUMA system is developed. The NCC-NUMA card is directly plugged into the PCI slot of each node, and contains shared memory, network cache, shared memory control module and network control module. The network cache is maintained for the shared memory on the PCI bus of cluster nodes. The coherency mechanism between the network cache and the shared memory is based on the IEEE SCI standard. According to the SPLASH-2 benchmark experiments, the NCC-NUMA system showed improvements of 56% compared with an SCI-based cluster without network cache.