• Korean Journal of Mathematics
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• v.20 no.4
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• pp.423-431
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• 2012

There have been some study characterizing monoids by homological classification using the properties around projectivity, injectivity, or regularity of acts. In particular Kilp and Knauer([4]) have analyzed monoids over which all acts with one of the properties around projectivity or injectivity are regular. However Kilp and Knauer left over problems of characterization of monoids over which all regular right S-acts are (weakly) at, (weakly) injective or faithful. Among these open problems, Liu([3]) proved that all regular right S-acts are (weakly) at if and only if es is a von Neumann regular element of S for all $s{\in}S$ and $e^2=e{\in}T$, and that all regular right S-acts are faithful if and only if all right ideals eS, $e^2=e{\in}T$, are faithful. But it still remains an open question to characterize over which all regular right S-acts are weakly injective or injective. Hence the purpose of this study is to investigate the relations between regular right S-acts and weakly injective right S-acts, and then characterize the monoid over which all regular right S-acts are weakly injective.

• Journal of the Korean Institute of Gas
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• v.25 no.4
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• pp.10-18
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• 2021

CO₂ storage technology in an aquifer is one of the most effective way to decrease global warming due to a high storage capacity and economics. A demonstration-scale offshore CO₂ storage project was performed in a geological deep aquifer in the Pohang Basin, Korea for a technological development of large-scale CO₂ storage. A challenging issue in the early design stage of the project was to establish the proper injectivity during CO₂ injection. To solve this issue, injection conditions were calculated by calculating injection rate, pressure, temperature, CO₂ phase change, and thermodynamic properties. For this study, we simulated and numerically analyzed CO₂ phase change from gas to supercritical phase and flow behavior in transport piping and injection tubing using OLGA program. Our results provide the injectivity conditions of CO₂ injection system combined with a bottomhole pressure of an aquifer.

• Bulletin of the Korean Mathematical Society
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• v.57 no.2
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• pp.371-381
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• 2020

A ring R is called right pure-injective if it is injective with respect to pure exact sequences. According to a well known result of L. Melkersson, every commutative Artinian ring is pure-injective, but the converse is not true, even if R is a commutative Noetherian local ring. In this paper, a series of conditions under which right pure-injective rings are either right Artinian rings or quasi-Frobenius rings are given. Also, some of our results extend previously known results for quasi-Frobenius rings.

• Kyungpook Mathematical Journal
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• v.49 no.2
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• pp.389-392
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• 2009

The purpose of this note is to improve several known results on GQ-injective rings. We investigate in this paper the von Neumann regularity of left GQ-injective rings. We give an answer a question of Ming in the positive. Actually it is proved that if R is a left GQ-injective ring whose simple singular left R-modules are GP-injective then R is a von Neumann regular ring.

• Kyungpook Mathematical Journal
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• v.62 no.4
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• pp.641-655
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• 2022

A right R-module N is called pseudo semisimple-M-injective if for any monomorphism from every semisimple submodule of M to N, can be extended to a homomorphism from M to N. In this paper, we study some properties of pseudo semisimple-injective modules. Moreover, some results of pseudo semisimple-injective modules over formal triangular matrix rings are obtained.

• Korean Journal of Mathematics
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• v.4 no.1
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• pp.45-49
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• 1996

Let $F_0$ be the maximal real subfield of $\mathbb{Q}({\zeta}_q+{\zeta}_q^{-1})$ and $F_{\infty}={\cup}_{n{\geq}0}F_n$ be its basic $\mathbb{Z}_p$-extension. Let $A_n$ be the Sylow $p$-subgroup of the ideal class group of $F_n$. The aim of this paper is to examine the injectivity of the natural $mapA_n{\rightarrow}A_m$ induced by the inclusion $F_n{\rightarrow}F_m$ when $m>n{\geq}0$. By using cyclotomic units of $F_n$ and by applying cohomology theory, one gets the following result: If $p$ does not divide the order of $A_1$, then $A_n{\rightarrow}A_m$ is injective for all $m>n{\geq}0$.

• Journal of the Korean Institute of Gas
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• v.28 no.2
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• pp.66-75
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• 2024

This paper presents development of a CO₂ injectivity analysis model using nodal analysis for the depleted oil reservoirs in Malaysia. Based on the final well report of an appraisal well, a basic model was established, and sensitivity analysis was performed on injection pressure, tubing size, reservoir pressure, reservoir permeability, and thickness. Utilizing the well testing report of A appraisal well, permeability of 10md was determined through production nodal analysis. Using the basic input data from the A appraisal well, an injection well model was set. Nodal analysis of the basic model, at the bottomhole pressure of 3000.74psia, estimated the CO₂ injection rate to be 13.29MMscfd. As the results of sensitivity analysis, the injection pressure, reservoir thickness, and permeability tend to exhibit a roughly linear increase in injection rate when they were higher, while a decrease in reservoir pressure at injection also resulted in an approximate linear increase in injection rate. Analyzing the injection rate per inch of tubing size, the optimal tubing size of 2.548inch was determined. It is recommended that if the formation parting pressure is known, performing nodal analysis can predict the maximum reservoir pressure and injection pressure by comparing with bottomhole pressure.

• 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.

• Bulletin of the Korean Mathematical Society
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• v.56 no.2
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• pp.439-450
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• 2019

Let R be a ring with unity. Given modules $M_R$ and $_RN$, $M_R$ is said to be absolutely $_RN$-pure if $M{\otimes}N{\rightarrow}L{\otimes}N$ is a monomorphism for every extension $L_R$ of $M_R$. For a module $M_R$, the subpurity domain of $M_R$ is defined to be the collection of all modules $_RN$ such that $M_R$ is absolutely $_RN$-pure. Clearly $M_R$ is absolutely $_RF$-pure for every flat module $_RF$, and that $M_R$ is FP-injective if the subpurity domain of M is the entire class of left modules. As an opposite of FP-injective modules, $M_R$ is said to be a test for flatness by subpurity (or t.f.b.s. for short) if its subpurity domain is as small as possible, namely, consisting of exactly the flat left modules. Every ring has a right t.f.b.s. module. $R_R$ is t.f.b.s. and every finitely generated right ideal is finitely presented if and only if R is right semihereditary. A domain R is $Pr{\ddot{u}}fer$ if and only if R is t.f.b.s. The rings whose simple right modules are t.f.b.s. or injective are completely characterized. Some necessary conditions for the rings whose right modules are t.f.b.s. or injective are obtained.

• Journal of the Korean Institute of Gas
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• v.27 no.1
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• pp.23-32
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• 2023

In this study, the Al₂O₃ nanofluid was synthesized as an additive for improving the injection efficiency and storage capacity of carbon dioxide (CO₂) in a depleted sandstone reservoir or deep saline aquifer. As the base fluid, deionized water (DIW) and saline prepared by referring to the composition of API Brine were used, and the fluid was synthesized by using Al₂O₃ nanofluid with CTAB (cetyltrimethyl-ammonium bromide), a cationic surfactant. After that, the dispersion stability was evaluated by using visual observation, dynamic light scattering (DLS), transmission electron microscope (TEM), and miscibility test. As a result, it was presented that stable nanofluid without agglomeration and precipitation after reaction with 70,000 ppm of brine could be synthesized when the nanoparticle concentration was 0.05 wt% or less.