• Journal of the Korean Mathematical Society
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• v.38 no.5
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• pp.987-1030
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• 2001

Some discrimination of modules whose endomorhism rings are prime is introduced, by means of structures of submodules inducing prime ideals of the endomorphism ring End(sub)R (M) of a left R-module (sub)RM over a ring R. Modules with non-prime endomorphism rings are contrapositively studied as well.

• Bulletin of the Korean Mathematical Society
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• v.32 no.2
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• pp.349-357
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• 1995

In the theory of elliptic curves over a complete field with bad reduction (i.e. with nonintegral j-invariant) Tate elliptic curves play an important role. Likewise, in the theory of Drinfeld modules, Tate-Drinfeld modules replace Tate elliptic curves.

• Bulletin of the Korean Mathematical Society
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• v.55 no.2
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• pp.499-505
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• 2018

In this paper, we show that the co-localization of co-Cohen Macaulay modules preserves co-Cohen Macaulayness under a certain condition. In addition, we give a characterization of co-Cohen Macaulay modules by vanishing properties of the dual Bass numbers of modules.

• Korean Journal of Mathematics
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• v.16 no.3
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• pp.281-290
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• 2008

The purpose of this paper, GM modules are defined as a generalization of AGR rings. Also, from the faithful GM-property, we get a commutativity of rings. Finally, for a nearring R, we will introduce MR groups, and also derive some properties of GM modules and MR groups.

• Honam Mathematical Journal
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• v.36 no.2
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• pp.339-344
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• 2014

In this paper, we give some properties on projective modules, locally cyclic projective modules and the ideal ${\tau}(M)$.

• Bulletin of the Korean Mathematical Society
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• v.38 no.1
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• pp.121-128
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• 2001

In this paper, we define Jacobson modules which are the generalization of Jacobson rings. We give criteria of Jacobson modules and useful properties of Jacobson modules.

• Bulletin of the Korean Mathematical Society
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• v.43 no.4
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• pp.755-762
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• 2006

For a commutative ring R and an injective cogenerator E in the category of R-modules, we characterize von Neumann regular rings and semisimple artinian rings in terms of the properties of dual modules with respect to E.

• Communications of the Korean Mathematical Society
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• v.34 no.1
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• pp.95-103
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• 2019

In this paper we study certain modules whose prime spectrums are Noetherian or/and spectral spaces. In particular, we investigate the relationship between topological properties of prime spectra of torsion modules and algebraic properties of them.

• Proceedings of the KIEE Conference
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• 2000.07d
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• pp.2784-2786
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• 2000

Mobile robots include control modules for autonomous obstacle avoidance and navigation. They are range modules to detect and avoid obstacles. motor control modules to operate two wheels. and encoder modules for localization. There is needed an appropriate controller for each modules. In this paper. a control system. including 18 channels for Sonar sensors. 4 channels for PWM modules. and 4 channels for encoder modules. is proposed using TMS320C32 DSP adopted with CAN. The board communicates with other modules by CAN. so that mobile robots can perform several tasks in real time. So we can realize on autonomous mobile robot with basic functions such as obstacle avoidance by using the developed controller. Especially. this controller has 100 msec scan time for 16 sonar sensors and can detect closer objects comparing with standard sonar sensors.

• 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.