• Bulletin of the Korean Mathematical Society
• /
• v.60 no.4
• /
• pp.1071-1083
• /
• 2023

The main motivation of this paper is to introduce and study the notions of strong Dedekind rings and semi-regular injective modules. Specifically, a ring R is called strong Dedekind if every semi-regular ideal is Q₀-invertible, and an R-module E is called a semi-regular injective module provided Ext¹_R(T, E) = 0 for every 𝓠-torsion module T. In this paper, we first characterize rings over which all semi-regular injective modules are injective, and then study the semi-regular injective envelopes of R-modules. Moreover, we introduce and study the semi-regular global dimensions sr-gl.dim(R) of commutative rings R. Finally, we obtain that a ring R is a DQ-ring if and only if sr-gl.dim(R) = 0, and a ring R is a strong Dedekind ring if and only if sr-gl.dim(R) ≤ 1, if and only if any semi-regular ideal is projective. Besides, we show that the semi-regular dimensions of strong Dedekind rings are at most one.

• Communications of the Korean Mathematical Society
• /
• v.21 no.1
• /
• pp.37-43
• /
• 2006

We prove that $M_1\longrightarrow^f\;M_2$ is an injective representation of a quiver $Q={\bullet}{\rightarrow}{\bullet}$ if and only if $M_1\;and\;M_2$ are injective left R-modules, $M_1\longrightarrow^f\;M_2$ is isomorphic to a direct sum of representation of the types $E_l{\rightarrow}0$ and $M_1\longrightarrow^{id}\;M_2$ where $E_l\;and\;E_2$ are injective left R-modules. Then, we generalize the result so that a representation$M_1\longrightarrow^{f_1}\;M_2\; \longrightarrow^{f_2}\;\cdots\;\longrightarrow^{f_{n-1}}\;M_n$ of a quiver $Q={\bullet}{\rightarrow}{\bullet}{\rightarrow}{\cdots}{\rightarrow}{\bullet}$ is an injective representation if and only if each $M_i$ is an injective left R-module and the representation is a direct sum of injective representations.

• Korean Journal of Mathematics
• /
• v.21 no.4
• /
• pp.463-471
• /
• 2013

Let R be a ring with identity 1, $I(R){\neq}\{0\}$ be the set of all nonunit idempotents in R, and M(R) be the set of all primitive idempotents and 0 of R. We say that I(R) is additive if for all e, $f{\in}I(R)$ ($e{\neq}f$), $e+f{\in}I(R)$. In this paper, the following are shown: (1) I(R) is a finite additive set if and only if $M(R){\backslash}\{0\}$ is a complete set of primitive central idempotents, char(R) = 2 and every nonzero idempotent of R can be expressed as a sum of orthogonal primitive idempotents of R; (2) for a regular ring R such that I(R) is a finite additive set, if the multiplicative group of all units of R is abelian (resp. cyclic), then R is a commutative ring (resp. R is a finite direct product of finite field).

• Journal of Satellite, Information and Communications
• /
• v.2 no.2
• /
• pp.64-68
• /
• 2007

This paper describes the development of RF front.end equipment of a wide band high precision satellite navigation receiver to be able to receive the currently available GPS navigation signal and the GALILEO navigation signal to be developed in Europe in the near future. The wide band satellite navigation receiver with high precision performance is composed of L - band antenna, RF/IF converters for multi - band navigation signals, and high performance baseband processor. The L - band satellite navigation antenna is able to be received the signals in the range from 1.1 GHz to 1.6 GHz and from the navigation satellite positioned near the horizon. The navigation signal of GALILEO navigation satellite consists of L1, E5, and E6 band with signal bandwidth more than 20 MHz which is wider than GPS signal. Due to the wide band navigation signal, the IF frequency and signal processing speed should be increased. The RF/IF converter has been designed with the single stage downconversion structure, and the IF frequency of 140 MHz has been derived from considering the maximum signal bandwidth and the sampling frequency of 112 MHz to be used in ADC circuit. The final output of RF/IF converter is a digital IF signal which is generated from signal processing of the AD converter from the IF signal. The developed RF front - end has the C/N0 performance over 40dB - Hz for the - 130dBm input signal power and includes the automatic gain control circuits to provide the dynamic range over 40dB.

• The Journal of Society for e-Business Studies
• /
• v.7 no.1
• /
• pp.1-17
• /
• 2002

Business environment for e-commerce companies have been rapidly changed for the last several yens and they have found out that strategic alliance as one of the important and practical means to cope with the dynamic environment. Despite the increasing number of e-commerce company's strategic alliances during last several years, there have been few studies made on strategic alliance which reflect the e-commerce company's uniqueness： dynamism, time to market, If-based business, etc. In order to reflect this uniqueness, we attempt to derive guidelines of alliance process for e-commerce companies in three aspects： 1) resource system analysis, 2) value chain analysis, and 3) If-based strategic alliance implementation and management. Finally, we propose the integrated process of strategic alliance for e-commerce companies including those proposed guidelines.

• Bulletin of the Korean Mathematical Society
• /
• v.61 no.3
• /
• pp.797-811
• /
• 2024

In this paper, we define the torsion graph determined by equivalence classes of torsion elements and denote it by A_E(M). The vertex set of A_E(M) is the set of equivalence classes {[x] | x ∈ T(M)^*}, where two torsion elements x, y ∈ T(M)^* are equivalent if ann(x) = ann(y). Also, two distinct classes [x] and [y] are adjacent in A_E(M), provided that ann(x)ann(y)M = 0. We shall prove that for every torsion finitely generated module M over a Dedekind domain R, a vertex of A_E(M) has degree two if and only if it is an associated prime of M.

• The Plant Pathology Journal
• /
• v.23 no.4
• /
• pp.281-286
• /
• 2007

Interactions between viral proteins and host proteins are essential for virus replication. Especially, translation of viral genes completely depends on the host machinery. In potyviruses, interactions of genome-linked viral protein (VPg) with host translation factors including eIF4E, eIF(iso)4E, and poly(A)-binding protein (PABP) has previously been characterized. In this study, we investigated interactions between Soybean mosaic virus (SMV) viral proteins and host translation factors by yeast two-hybrid system. SMV VPg interacted with eIF4E, eIF(iso)4E, and PABP in yeast two-hybrid system, while SMV helper component proteinase (HC-pro) interacted with neither of those proteins. The interaction between SMV NIb and PABP was also detected. These results are consistent with those reported previously in other potyviruses. Interestingly, we found reproducible and specific interactions between SMV coat protein (CP) and PABP. Deletion analysis showed that the region of CP comprising amino acids 116 to 206 and the region of PABP comprising amino acids 520 to 580 are involved in CP/PABP interactions. Soybean library screening with SMV NIb by yeast two-hybrid assay also identified several soybean proteins including chlorophyll a/b binding preprotein, photo-system I-N subunit, ribulose 1,5-biphosphate carboxylase, ST-LSI protein, translation initiation factor 1, TIR-NBS type R protein, RNA binding protein, ubiquitin, and LRR protein kinase. Altogether, these results suggest that potyviral replicase may comprise a multi-protein complex with PABP, CP, and other host factors.

• Bulletin of the Korean Mathematical Society
• /
• v.48 no.5
• /
• pp.1033-1039
• /
• 2011

Let R be a ring with identity 1, I(R) be the set of all idempotents in R and G be the group of all units of R. In this paper, we show that for any semiperfect ring R in which 2 = 1+1 is a unit, I(R) is closed under multiplication if and only if R is a direct sum of local rings if and only if the set of all minimal idempotents in R is closed under multiplication and eGe is contained in the group of units of eRe. In particular, for a left Artinian ring in which 2 is a unit, R is a direct sum of local rings if and only if the set of all minimal idempotents in R is closed under multiplication.

• Journal of applied mathematics & informatics
• /
• v.17 no.1_2_3
• /
• pp.567-572
• /
• 2005

A Banach space X is a Hilbert space if and only if $$E{\mid}x=Y{\mid}{\le}2$$ for all x$\in$ X and all X-valued Bochner integrable functions Y satisfying EY = 0 and ${\mid}x-Y{\mid}{\le}2$ a.e.

• Communications of the Korean Mathematical Society
• /
• v.11 no.2
• /
• pp.295-301
• /
• 1996

In this paper we will define correct module and strongly correct module. We can have some basic results about those modules. And we will show that M is a graded correct R-module if and only if $M_e$ is a correct $R_e$-module.