• Kyungpook Mathematical Journal
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• 제56권1호
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• pp.83-94
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• 2016

Let M and N be modules over a ring R. The purpose of this paper is to study modules M, N for which the bi-module [M, N] is regular or pi. It is proved that the bi-module [M, N] is regular if and only if a module N is semi M-projective and $Im({\alpha}){\subseteq}^{\oplus}N$ for all ${\alpha}{\in}[M,N]$, if and only if a module M is semi N-injective and $Ker({\alpha}){\subseteq}^{\oplus}N$ for all ${\alpha}{\in}[M,N]$. Also, it is proved that the bi-module [M, N] is pi if and only if a module N is direct M-projective and for any ${\alpha}{\in}[M,N]$ there exists ${\beta}{\in}[M,N]$ such that $Im({\alpha}{\beta}){\subseteq}^{\oplus}N$, if and only if a module M is direct N-injective and for any ${\alpha}{\in}[M,N]$ there exists ${\beta}{\in}[M,N]$ such that $Ker({\beta}{\alpha}){\subseteq}^{\oplus}M$. The relationship between the Jacobson radical and the (co)singular ideal of [M, N] is described.

• Korean Journal of Mathematics
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• 제23권3호
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• pp.357-370
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• 2015

In this paper, we introduce the concept of (m, n)-ideals in a non-associative ordered structure, which is called an ordered Abel-Grassmann's groupoid, by generalizing the concept of (m, n)-ideals in an ordered semigroup [14]. We also study the (m, n)-regular class of an ordered AG-groupoid in terms of (m, n)-ideals.

• 대한수학회보
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• 제50권6호
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• pp.1855-1861
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• 2013

Let R be a commutative Noetherian ring, I an ideal of R, M and N two R-modules. We characterize the least integer i such that $H^i_I(M,N)$ is not weakly Artinian by using the notion of weakly filter regular sequences. Also, a local-global principle for minimax generalized local cohomology modules is shown and the result generalizes the corresponding result for local cohomology modules.

• 대한수학회보
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• 제55권2호
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• pp.675-677
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• 2018

• Korean Journal of Mathematics
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• 제16권3호
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• pp.379-388
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• 2008

We introduce countably strong inclusions ${\triangleleft}=({\triangleleft}_1,\;{\triangleleft}_2)$ on a biframe $L=(L_0,\;L_1,\;L_2)$ and i-strongly regular ${\sigma}$-ideals (i =1, 2) and then using them, we construct biframe $Lindel{\ddot{o}}fication$ of L. Furthermore, we obtain a sufficient condition for which L has a unique countably strong inclusion.

• Kyungpook Mathematical Journal
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• 제54권2호
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• pp.321-332
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• 2014

In this article we introduce different types of multiplier I-convergent double sequence spaces. We study their different algebraic and topological properties like solidity, symmetricity, completeness etc. The decomposition theorem is established and some inclusion results are proved.

• 대한수학회논문집
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• 제17권3호
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• pp.409-422
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• 2002

We investigate the relationship between various generalizations of von Neumann regularity condition and the condition that every prime ideal is maximal in exchange rings.

• 한국지진공학회:학술대회논문집
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• 한국지진공학회 1998년도 춘계 학술발표회 논문집 Proceedings of EESK Conference-Spring 1998
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• pp.163-170
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• 1998

The influence of the dam-reservoir interaction on the seismic response of dams is studied. The impounded water is assumed to be inviscid and compressible ideal fluid. Material damping is introduce to simulate the energy loss of wave propagation in the water. The irregular region of the impounded water adjacent to the dam is modeled by boundary element method. The regular region extending to infinity is modeled by the transmitting boundary. The dam body is assumed to behave elastically and modeled by finite element method. The coupled equation of motion is obtained by substructure method.

• 대한수학회보
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• 제30권1호
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• pp.61-64
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• 1993

In this paper, we show that if R is a local-global domain then the Question holds. McDonald and Waterhouse in [6] and Estes and Guralnick in [5] introduced the concept of local-global rings (so called rings with many units) independently. A local-global ring is a commutative ring R with 1 satisfying; if a polynomial f in R[ $x_{1}$, .., $x_{n}$] represents a unit over $R_{P}$ for every maximal ideal P in R, then f represents a unit over R. Such rings include semilocal rings, or more generally, rings which are von Neumann regular mod their Jacobson radical, and the ring of all algebraic integers.s.s.

• 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.