• Bulletin of the Korean Mathematical Society
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• v.56 no.2
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• pp.373-382
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• 2019

In this note, we mainly discuss strongly Gorenstein hereditary rings. We prove that for any ring, the class of SG-projective modules and the class of G-projective modules coincide if and only if the class of SG-projective modules is closed under extension. From this we get that a ring is an SG-hereditary ring if and only if every ideal is G-projective and the class of SG-projective modules is closed under extension. We also give some examples of domains whose ideals are SG-projective.

• Bulletin of the Korean Mathematical Society
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• v.58 no.5
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• pp.1221-1233
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• 2021

In this paper, we introduce and investigate a new class of modules that is closely related to the class of Noetherian modules. Let R be a commutative ring and M be an R-module. We say that M is an r-Noetherian module if every r-submodule of M is finitely generated. Also, we call the ring R to be an r-Noetherian ring if R is an r-Noetherian R-module, or equivalently, every r-ideal of R is finitely generated. We show that many properties of Noetherian modules are also true for r-Noetherian modules. Moreover, we extend the concept of weakly Noetherian rings to the category of modules and we characterize Noetherian modules in terms of r-Noetherian and weakly Noetherian modules. Finally, we use the idealization construction to give non-trivial examples of r-Noetherian rings that are not Noetherian.

• Bulletin of the Korean Mathematical Society
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• v.56 no.4
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• pp.961-976
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• 2019

Let R be any commutative ring and S be any multiplicative closed set. We introduce an S-version of $\mathcal{F}$-Mittag-Leffler modules, called $\mathcal{F}_{\mathcal{S}}$-Mittag-Leffler modules, and define the projective dimension with respect to these modules. We give some characterizations of $\mathcal{F}_{\mathcal{S}}$-Mittag-Leffler modules, investigate the relationships between $\mathcal{F}$-Mittag-Leffler modules and $\mathcal{F}_{\mathcal{S}}$-Mittag-Leffler modules, and use these relations to describe noetherian rings and coherent rings, such as R is noetherian if and only if $R_S$ is noetherian and every $\mathcal{F}_{\mathcal{S}}$-Mittag-Leffler module is $\mathcal{F}$-Mittag-Leffler. Besides, we also investigate the $\mathcal{M}^{\mathcal{F}_{\mathcal{S}}$-global dimension of R, and prove that $R_S$ is noetherian if and only if its $\mathcal{M}^{\mathcal{F}_{\mathcal{S}}$-global dimension is zero; $R_S$ is coherent if and only if its $\mathcal{M}^{\mathcal{F}_{\mathcal{S}}$-global dimension is at most one.

• Smart Structures and Systems
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• v.22 no.2
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• pp.167-174
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• 2018

Digital input and output modules are widely used to connect digital sensors and actuators to automation systems. Digital I/O modules provide flexible connectivity extension to numerous sensors and actuators and protect systems from high voltages and currents by isolation. Components in digital I/O modules are inevitably affected by operating and environmental conditions, such as high voltage, high current, high temperature, and temperature cycling. Because digital I/O modules transfer signals or isolate the systems from unexpected voltage and current transients, their failures may result in signal transmission failures and damages to sensitive circuitry leading to system malfunction and system shutdown. In this study, the lifetime of optocouplers, one of the critical components in digital I/O modules, was predicted using Bayesian tracking approaches. Accelerated degradation tests were conducted for collecting the critical performance parameter of optocouplers, current transfer ratio (CTR), during their lifetime. Bayesian tracking approaches, including extended Kalman filter and particle filter, were applied to predict the failure. The performance of each prognostic algorithm was then compared using accuracy and robustness-based performance metrics.

• The Journal of Korea Robotics Society
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• v.11 no.3
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• pp.163-171
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• 2016

A modular manipulator in serial-chain structure usually consists of a series of modularized revolute joint and link modules. The geometric shapes of these modules affect the number of possible configurations of modular manipulator after assembly. Therefore, it is important to design the geometry of the joint and link modules that allow various configurations of the manipulators with minimal set of modules. In this paper, a new 1-DoF(degree of freedom) joint module and simple link modules are designed based on a methodology of joint configurations using a series of Rotational(type-R) and Twist(type-T) joints. Two of the joint modules can be directly connected so that two types of 2-DoFs joints could be assembled without a link module between them. The proposed geometries of joint and link modules expand the possible configurations of assembled modular manipulators compared to existing ones. Modular manipulator system of this research can be a cornerstone of user-centered markets with various solution but low-cost, compared to conventional manipulators of fixed-configurations determined by the provider.

• Honam Mathematical Journal
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• v.38 no.2
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• pp.259-267
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• 2016

A module M over an associative ring R with unity is a QTAG-module if every finitely generated submodule of any homomorphic image of M is a direct sum of uniserial modules. Recently, the authors introduced the classes of QTAG-modules namely as socle-regular and strongly socle-regular QTAG-modules which properly contain the classes of transitive and fully transitive QTAG-modules respectively. Here we define strongly and quasi transitivities and study the inter relations between various type of transitivities.

• Honam Mathematical Journal
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• v.21 no.1
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• pp.1-12
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• 1999

The height of a prime submodule and a module version of the Krull dimension are studied.

• Bulletin of the Korean Mathematical Society
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• v.61 no.1
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• pp.1-12
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• 2024

In this paper, we introduce the notion of Gorenstein (m, n)-flat modules as an extension of (m, n)-flat left R-modules over a ring R, where m and n are two fixed positive integers. We demonstrate that the class of all Gorenstein (m, n)-flat modules forms a Kaplansky class and establish that (𝓖𝓕_m,n(R),𝓖𝓒_m,n(R)) constitutes a hereditary perfect cotorsion pair (where 𝓖𝓕_m,n(R) denotes the class of Gorenstein (m, n)-flat modules and 𝓖𝓒_m,n(R) refers to the class of Gorenstein (m, n)-cotorsion modules) over slightly (m, n)-coherent rings.

• Journal of Gifted/Talented Education
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• v.19 no.1
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• pp.187-205
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• 2009

The purpose of this study was to investigate the perception of science high school students for modeling module that contain scientists' thinking process. Modeling modules about 'gas diffusion', 'ion conductivity' and 'ion mobility' were applied to science high school students. Interview, lab report, and dialogue were analyzed to comprehend features of modeling module. Students who performed modeling modules perceived that modeling modules were appropriate to experience scientists' research process. Modeling modules were kind of activity to raise 'muscle of thinking', to be needed 'new views' and 'various representations', and to contain 'designing laboratory process'. Therefore, the development of various modeling modules is needed in the near future.

• Honam Mathematical Journal
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• v.43 no.2
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• pp.199-207
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• 2021

In this paper we introduce two classes of modules namely e-symmetric and e-reduced. Also, we study the characterizations of e-symmetric and e-reduced modules and their related properties.