• Honam Mathematical Journal
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• v.31 no.4
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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.

• Journal of the Chungcheong Mathematical Society
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• v.24 no.3
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• pp.553-560
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• 2011

We introduce a method to construct some algebras $R{\in}MC_n(k)$ with dim(R) = n and $dim(m_R^2)=1$ for each $n{\geq}3$.

• Journal of applied mathematics & informatics
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• v.17 no.1_2_3
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• pp.605-614
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• 2005

We show that an Artinian O-sequence $h_0,h_1,{\cdots},h_{d-1},h_d\;=\;h_{d-1},h_{d+l}\;>\;h_d$ of codimension 3 is not level when $h_{d-1}\;=\;h_d\;=\;d + i\;and\;h{d+1}\;=\;d+(i+1)\;for\;i\;=\;1,\;2,\;and\;3$, which is a partial answer to the question in [9]. We also introduce an algorithm for finding noncancelable Betti numbers of minimal free resolutions of all possible Artinian O-sequences based on the theorem of Froberg and Laksov in [2].

• Bulletin of the Korean Mathematical Society
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• v.54 no.6
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• pp.2029-2041
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• 2017

The main aim of this article is to study symmetric (v, k, ${\lambda}$) designs admitting a flag-transitive and point-primitive automorphism group G whose socle is PSU(3, q). We indeed show that such designs must be complete.

• Kyungpook Mathematical Journal
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• v.46 no.4
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• pp.597-601
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• 2006

We introduce in this paper the concept of idempotent reflexive right ideals and concern with rings containing an injective maximal right ideal. Some known results for reflexive rings and right HI-rings can be extended to idempotent reflexive rings. As applications, we are able to give a new characterization of regular right self-injective rings with nonzero socle and extend a known result for right weakly regular rings.

• Communications of the Korean Mathematical Society
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• v.18 no.4
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• pp.629-633
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• 2003

We investigate in this paper rings containing a finitely generated p-injective maximal left ideal. We show that if R is a semiprime ring containing a finitely generated p-injective maximal left ideal, then R is a left p-injective ring. Using this result we are able to give a new characterization of von Neumann regular rings with nonzero socle.

• Bulletin of the Korean Mathematical Society
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• v.58 no.1
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• pp.147-161
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• 2021

In this paper, we introduced and studied sa-supplement submodules. A submodule U of a module V is called an sa-supplement submodule in V if there exists a submodule T of V such that V = T + U and U ∩ T is semiartinian. The class of sa-supplement sequences ������ is a proper class which is generated by socle-free modules injectively. We studied modules that have an sa-supplement in every extension, modules whose all submodules are sa-supplement and modules whose all sa-supplement submodules are direct summand. We provided new characterizations of right semiartinian rings and right SSI rings.

• Communications of Mathematical Education
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• v.34 no.2
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• pp.135-160
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• 2020

The purpose of this study is to draw implications for improving the method of reflecting the competencies in Korea mathematics curriculum, by analyzing what competencies are reflected in foreign mathematics and curriculum. As a result of the study, foreign countries were reflecting their competencies in mathematics curriculum in various ways. In France mathematics curriculum, the achievement standards of learning competencies(compétences travaillées) that students should reach by cycle were presented, and the related common competencies(socle commun) were indicated. In Australia's mathematics curriculum, the general capabilities for achievement standards were identified, and the achievement criteria for proficiency strands to be reached by grade level were presented. British Columbia's mathematics curriculum actively reflected its competencies. In the mathematics curriculum, domains were reorganized based on the competencies, and achievement standards of the competencies were proposed. The results of this study will help in improving the ways in which were reflected competencies in mathematics curriculum.

• Bulletin of the Korean Mathematical Society
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• v.56 no.1
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• pp.83-102
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• 2019

For $M{\in}R-Mod$, $N{\subseteq}M$ and $L{\in}{\sigma}[M]$ we consider the product $N_ML={\sum}_{f{\in}Hom_R(M,L)}\;f(N)$. A module $N{\in}{\sigma}[M]$ is called an M-multiplication module if for every submodule L of N, there exists a submodule I of M such that $L=I_MN$. We extend some important results given for multiplication modules to M-multiplication modules. As applications we obtain some new results when M is a semiprime Goldie module. In particular we prove that M is a semiprime Goldie module with an essential socle and $N{\in}{\sigma}[M]$ is an M-multiplication module, then N is cyclic, distributive and semisimple module. To prove these results we have had to develop new methods.

• Kyungpook Mathematical Journal
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• v.61 no.2
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• pp.239-248
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• 2021

In this paper we study modules with the W F I⁺-extending property. We prove that if M satisfies the W F I⁺-extending, pseudo duo properties and M/(Soc M) has finite uniform dimension then M decompose into a direct sum of a semisimple submodule and a submodule of finite uniform dimension. In particular, if M satisfies the W F I⁺-extending, pseudo duo properties and ascending chain (respectively, descending chain) condition on essential submodules then M = M₁ ⊕ M₂ for some semisimple submodule M₁ and Noetherian (respectively, Artinian) submodule M₂. Moreover, we show that if M is a W F I-extending module with pseudo duo, C₂ and essential socle then the quotient ring of its endomorphism ring with Jacobson radical is a (von Neumann) regular ring. We provide several examples which illustrate our results.