• Honam Mathematical Journal
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• 제31권4호
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• pp.529-540
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• 2009

The authors have investigated several properties of endomorphism rings of modules. In particular, a closedly simple module and a closedly semi-simple module were defined and then the regularities of its rings of endomorphisms were discussed.

• Kyungpook Mathematical Journal
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• 제63권4호
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• pp.521-537
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• 2023

A module M is called a simple-direct-injective module if, whenever A and B are simple submodules of M with A ≅ B and B is a direct summand of M, then A is a direct summand of M. Some new characterizations of these modules are proved. The structure of simple-direct-injective modules over a commutative Dedekind domain is fully determined. Also, some relevant counterexamples are indicated to show that a left simple-direct-injective ring need not be right simple-direct-injective.

• Bulletin of the Korean Mathematical Society
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• 제52권2호
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• pp.549-556
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• 2015

In this paper, we characterize w-Noetherian modules in terms of polynomial modules and w-Nagata modules. Then it is shown that for a finite type w-module M, every w-epimorphism of M onto itself is an isomorphism. We also define and study the concepts of w-Artinian modules and w-simple modules. By using these concepts, it is shown that for a w-Artinian module M, every w-monomorphism of M onto itself is an isomorphism and that for a w-simple module M, $End_RM$ is a division ring.

• Bulletin of the Korean Mathematical Society
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• 제60권2호
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• pp.339-348
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• 2023

It is shown that every nilpotent-invariant module can be decomposed into a direct sum of a quasi-injective module and a square-free module that are relatively injective and orthogonal. This paper is also concerned with rings satisfying every cyclic right R-module is nilpotent-invariant. We prove that R ≅ R₁ × R₂, where R₁, R₂ are rings which satisfy R₁ is a semi-simple Artinian ring and R₂ is square-free as a right R₂-module and all idempotents of R₂ is central. The paper concludes with a structure theorem for cyclic nilpotent-invariant right R-modules. Such a module is shown to have isomorphic simple modules eR and fR, where e, f are orthogonal primitive idempotents such that eRf ≠ 0.

• Journal of the Korean Mathematical Society
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• 제32권2호
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• pp.265-277
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• 1995

In [9], we gave a very explicit description of the injective envelope of an arbitray simple module over a polynomial ring $K[X_1, \ldots, X_n]$ over a field K in indeterminates $X_1, \ldots, X_n$. This paper presents another approach to give a description.

• Communications of the Korean Mathematical Society
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• 제18권4호
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• pp.615-620
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• 2003

Semi-meet-prime projective modules and fully invariant meet-prime submodules of a projective module are studied. Actually a generalization of the Schur's lemma and semi-prime endmorphism rings of projective modules are considered.

• Textile Coloration and Finishing
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• 제17권4호
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• pp.21-26
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• 2005

A combination separation system is composed of three parts, simple microfiltration unit for the pretreatment of real waste IPA, pervaporation unit with plate and frame type module(the effective membrane area 9,040$cm^2$), and simple ultrafiltration unit as a refiner. Utrafiltration module with hollow fiber membrane(MWCO 10,000) used to purify waste aqueous IPA solution. In addition, the flux of $CMPA-K^+$ composite membrane for waste aqueous IPA solution was very steady-state with long experiment time(30 days). And the standard deviation($\sigma$) was 0.152 and then the coefficient of variation($CV\%$)was 10.82 The IPA concentration on the membrane performance using pervaporation module system could be increased from $89.85wt(\%)$ to more than $99.90wt\%$ in about 8hr at operation temperature of $70^{\circ}C$ using the pervaporation module system. Therefore, a combination separation process system of simple filtration and pervaporation was very effective for the purpose of the IPA purification and reuse front industrial electronic components cleaning process.

• Journal of the Korean Mathematical Society
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• 제50권5호
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• pp.1051-1066
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• 2013

By utilizing known characterizations of ${\omega}$-Noetherian rings in terms of injective modules, we give more characterizations of ${\omega}$-Noetherian rings. More precisely, we show that a commutative ring R is ${\omega}$-Noetherian if and only if the direct limit of GV -torsion-free injective R-modules is injective; if and only if every R-module has a GV -torsion-free injective (pre)cover; if and only if the direct sum of injective envelopes of ${\omega}$-simple R-modules is injective; if and only if the essential extension of the direct sum of GV -torsion-free injective R-modules is the direct sum of GV -torsion-free injective R-modules; if and only if every $\mathfrak{F}_{w,f}(R)$-injective ${\omega}$-module is injective; if and only if every GV-torsion-free R-module admits an $i$-decomposition.

• Communications of the Korean Mathematical Society
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• 제10권3호
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• pp.575-581
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• 1995

The simple modules and the simple comodules of the quantum group $X)q(2)$ defined by M. L. Ge, N. H. Jing and Y. S. Wu, are classified.

• Aerospace Engineering and Technology
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• 제4권2호
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• pp.79-87
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• 2005

This paper describes a new on-board computer design for the next generation satellite. The new on-board computer utilizes centralized processing architecture with MCMERC325C CPU based on functional modular design concepts. The on-board computer consists of PM32 Module, TC-TM Module, IO Module and Power module. The IEEE-1355 DS/DE, or SpaceWire, provides a standard communication interface between module. It also provides simple cross-strap design for redundancy management and increases re-usability of the modules.