• Journal of applied mathematics & informatics
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• 제17권1_2_3호
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• pp.679-687
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• 2005

In this paper we shall give a new definition for a quasi-power module P(M) and discuss some properties for P(M). The quasi-power module P(M) is a direct sum of invertible quasi-submodules C(H)'s of P(M) and then the quasi-submodule C(H) is also a direct sum of strongly cyclic quasi-submodules of C(H). When M is a quasi-perfect right R-module, we shall see that the quasi-power module P(M) is invertible.

• Kyungpook Mathematical Journal
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• 제63권1호
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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.

• 한국정보통신학회논문지
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• 제17권3호
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• pp.634-640
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• 2013

기존의 패턴 및 데이터베이스 검색, 페이지 단위 문자열 검색 기법은 단순 검색 방식으로 오탐율이 많아 검색 결과에 대한 신뢰성이 떨어진다. 또한, 동일 조건을 다른 검색 기법에 추가로 시행함으로 인해 자원 낭비 및 시간 낭비를 초래하고 있다. 따라서 본 논문에서는 정규식 구문과 상관분석 기법의 통합적 연계 방식을 적용시킨 정보 검색 모듈을 개발하였다. 이를 통해 기존의 문자열 검색기법의 문제로 지적되어 온 오탐율을 줄임으로써 경제적인 효과 및 신뢰성을 확보하는 보안형 정보 검색 기술을 연구하였다.

• Korean Journal of Mathematics
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• 제22권1호
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• pp.151-167
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• 2014

Let M, N be modules over a ring R and $[M,N]=Hom_R(M,N)$. The concern is study of: (1) Some fundamental properties of [M, N] when [M, N] is regular or semipotent. (2) The substructures of [M, N] such as radical, the singular and co-singular ideals, the total and others has raised new questions for research in this area. New results obtained include necessary and sufficient conditions for [M, N] to be regular or semipotent. New substructures of [M, N] are studied and its relationship with the Tot of [M, N]. In this paper we show that, the endomorphism ring of a module M is regular if and only if the module M is semi-injective (projective) and the kernel (image) of every endomorphism is a direct summand.

• 호남수학학술지
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• 제38권2호
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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.

• Kyungpook Mathematical Journal
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• 제63권3호
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• pp.333-344
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• 2023

In this paper, we generalize the notions uniformly S-flat, briefly u-S-flat, modules and dimensions. We introduce and study the notions of weak u-S-flat modules. An R-module M is said to be weak u-S-flat if Tor^R₁ (R/I, M) is u-S-torsion for any ideal I of R. This new class of modules will be used to characterize u-S-von Neumann regular rings. Hence, we introduce the weak u-S-flat dimensions of modules and rings. The relations between the introduced dimensions and other (classical) homological dimensions are discussed.

• 호남수학학술지
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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.

• Korean Journal of Mathematics
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• 제7권2호
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• pp.215-218
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• 1999

We investigate characterizations of rings whose simple singular right R-modules are GP-injective. It is proved that if R is a semiprime ring whose simple singular right R-modules are GP-injective, then the center $Z(R)$ of R is a von Neumann regular ring. We consider the condition ($^*$): R satisfies $l(a){\subseteq}r(a)$ for any $a{\in}R$. Also it is shown that if R satisfies ($^*$) and every simple singular right R-module is GP-injective, then R is a reduced weakly regular ring.

• Kyungpook Mathematical Journal
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• 제46권4호
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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.

• 대한수학회지
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• 제38권5호
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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.