• Communications of the Korean Mathematical Society
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• v.32 no.3
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• pp.523-534
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• 2017

In this paper, we introduce two group graded types of $B{\acute{e}}zout$ modules, namely graded-$B{\acute{e}}zout$ modules and weakly graded-$B{\acute{e}}zout$ modules, which are two $B{\acute{e}}zout$ versions in Graded Module Theory. We investigate the relationship among the three types of $B{\acute{e}}zout$ modules, the ordinary $B{\acute{e}}zout$ modules and the two graded types of $B{\acute{e}}zout$ modules. Also, we study the structure of these new $B{\acute{e}}zout$ modules along with different properties; for instance, "A graded-$B{\acute{e}}zout$ R-module, with R being a Noetherian ring, is Noetherien iff it is gr-Noetherian".

• Research in Mathematical Education
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• v.13 no.3
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• pp.251-266
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• 2009

Being aware of the present situation in Latvia and in whole Europe, Mathematics curriculum development is a topical issue. One of the ways how to deal with it is the application of study modules in the study process. The division of Mathematics studies in the Forms and Content Modules allows students to understand better the organization of study process of mathematics, and creates conceptual awareness of Mathematics logics and its practical application helping students to understand causal relationships and to develop cognitive skills. In the article will be present same theoretical aspects and practical experience in Latvia University of Agriculture.

• Kyungpook Mathematical Journal
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• v.63 no.1
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• pp.15-27
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• 2023

A purely extending module is a generalization of an extending module. In this paper, we study several properties of purely extending modules and introduce the notion of purely essentially Baer modules. A module M is said to be a purely essentially Baer if the right annihilator in M of any left ideal of the endomorphism ring of M is essential in a pure submodule of M. We study some properties of purely essentially Baer modules and characterize von Neumann regular rings in terms of purely essentially Baer modules.

• Kyungpook Mathematical Journal
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• v.48 no.1
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• pp.63-71
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• 2008

In this paper, we study a module which is lifting and supplemented relative to a module class. Let R be a ring, and let X be a class of R-modules. We will define X-lifting modules and X-supplemented modules. Several properties of these modules are proved. We also obtain results for the case of specific classes of modules.

• Journal of the Korea Institute of Building Construction
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• v.13 no.6
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• pp.609-618
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• 2013

The unit modular construction system is a building technique in which unit modules are manufactured at a factory and then assembled at the construction site. It has many benefits, including reduction of the construction period and improvement in quality. For this reason, it is utilized for various purposes in Japan and England. While it has been introduced in Korea, there have been few Korean studies conducted on the unit modular system. In particular, little research has been done on the method of safely fixating the unit modules to a truck. Therefore, this study reviewed the fixation methods of unit modules for transport, analyzed the problems, and designed a fixation device for unit modules. In addition, a device for the fixation of unit modules to a truck was developed, and a structural simulation was implemented for a safety test by considering the maximum stress generated during the transport of the unit modules fixed on a truck. When the device for the fixation of unit modules is manufactured based on the results of the structural simulation done in this study, it is expected to aid the development of a more practical fixation device for unit modules.

• Kyungpook Mathematical Journal
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• v.54 no.2
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• pp.237-247
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• 2014

The purpose of this paper is to introduce the concept of strongly extending modules which are particular subclass of the class of extending modules, and study some basic properties of this new class of modules. A module M is called strongly extending if each submodule of M is essential in a fully invariant direct summand of M. In this paper we examine the behavior of the class of strongly extending modules with respect to the preservation of this property in direct summands and direct sums and give some properties of these modules, for instance, strongly summand intersection property and weakly co-Hopfian property. Also such modules are characterized over commutative Dedekind domains.

• East Asian mathematical journal
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• v.18 no.2
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• pp.245-259
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• 2002

In this paper, all rings or (left)near-rings R are associative, and for near-ring R, all R-groups are right R action and all modules are right R-modules. First, we begin with the study of rings in which all the additive endomorphisms or only the left multiplication endomorphisms are generated by ring endomorphisms and their properties. This study was motivated by the work on the Sullivan's Problem [14]. Next, for any right R-module M, we will introduce AM modules and investigate their basic properties. Finally, for any nearring R, we will also introduce MR-groups and study some of their properties.

• 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.

• Kyungpook Mathematical Journal
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• v.49 no.3
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• pp.557-562
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• 2009

A module M is said to be SIP-extending if the intersection of every pair of direct summands is essential in a direct summand of M. SIP-extending modules are a proper generalization of both SIP-modules and extending modules. Every direct summand of an SIP-module is an SIP-module just as a direct summand of an extending module is extending. While it is known that a direct sum of SIP-extending modules is not necessarily SIP-extending, the question about direct summands of an SIP-extending module to be SIP-extending remains open. In this study, we show that a direct summand of an SIP-extending module inherits this property under some conditions. Some related results are included about $C_{11}$ and SIP-modules.

• Bulletin of the Korean Mathematical Society
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• v.57 no.3
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• pp.691-707
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• 2020

In this paper, we introduce and study the notions of weakly ⊕-supplemented modules, weakly D2 modules and weakly D2-covers. A right R-module M is called weakly ⊕-supplemented if every non-small submodule of M has a supplement that is not essential in M, and module M_R is called weakly D2 if it satisfies the condition: for every s ∈ S and s ≠ 0, if there exists n ∈ ℕ such that sⁿ ≠ 0 and Im(sⁿ) is a direct summand of M, then Ker(sⁿ) is a direct summand of M. The class of weakly ⊕-supplemented-modules and weakly D2 modules contains ⊕-supplemented modules and D2 modules, respectively, and they are equivalent in case M is uniform, and projective, respectively.