• Bulletin of the Korean Mathematical Society
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• v.45 no.1
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• pp.59-66
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• 2008

Keskin and Harmanci defined the family B(M,X) = ${A{\leq}M|{\exists}Y{\leq}X,{\exists}f{\in}Hom_R(M,X/Y),\;Ker\;f/A{\ll}M/A}$. And Orhan and Keskin generalized projective modules via the class B(M, X). In this note we introduce X-local summands and X-hollow modules via the class B(M, X). Let R be a right perfect ring and let M be an X-lifting module. We prove that if every co-closed submodule of any projective module P contains Rad(P), then M has an indecomposable decomposition. This result is a generalization of Kuratomi and Chang's result [9, Theorem 3.4]. Let X be an R-module. We also prove that for an X-hollow module H such that every non-zero direct summand K of H with $K{\in}B$(H, X), if $H{\oplus}H$ has the internal exchange property, then H has a local endomorphism ring.

• Journal of the Korean Mathematical Society
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• v.47 no.4
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• pp.691-704
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• 2010

Over a ring R, let $P_R$ be a finitely generated projective right R-module. Then we define the G-injector (G-projector) if $P_R$ preservers Gorenstein injective modules (Gorenstein projective modules), the Gflator if $P_R$ preservers Gorenstein flat modules. G-injector (G-flator) and G-injector are characterized focus primarily on the cases where R is a Gorenstein ring, and under this condition we also study the relations between the injector (projector, flator) and the G-injector (G-projector, G-flator). Over any ring we also give the characteristics of G-injector (G-flator) by the Gorenstein injective (Gorenstein flat) dimensions of modules.

• Communications of the Korean Mathematical Society
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• v.33 no.2
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• pp.571-580
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• 2018

The object of the present paper is to prove the non-existence of pseudo projective Ricci symmetric spacetimes $(PW\;RS)_4$ with different types of energy momentum tensor. We also discuss whether a fluid $(PW\;RS)_4$ spacetime with the basic vector field as the velocity vector field of the fluid can admit heat flux. Next we consider perfect fluid and dust fluid $(PW\;RS)_4$ spacetimes respectively. Finally we construct an example of a $(PW\;RS)_4$ spacetime.

• Journal of the Korean Mathematical Society
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• v.31 no.4
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• pp.569-608
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• 1994

The subject matter of this survey has to do with holomorphic maps from a compact Riemann surface to projective space, which are also called algebrac curves; the theory we survey lies at the crossroads of function theory, projective geometry, and commutative algebra (although we should mention that the present survey de-emphasizes the algebraic aspect). Algebraic curves have been vigorously and continuously investigated since the time of Riemann. The reasons for the preoccupation with algebraic curves amongst mathematicians perhaps have to do with-other than the usual usual reason, namely, the herd mentality prompting us to follow the leads of a few great pioneering methematicians in the field-the fact that algebraic curves possess a certain simple unity together with a rich and complex structure. From a differential-topological standpoint algebraic curves are quite simple as they are neatly parameterized by a single discrete invariant, the genus. Even the possible complex structures of a fixed genus curve afford a fairly complete description. Yet there are a multitude of diverse perspectives (algebraic, function theoretic, and geometric) often coalescing to yield a spectacular result.

• Journal of Korean Society for Geospatial Information Science
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• v.10 no.2 s.20
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• pp.49-56
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• 2002

Many users of 3D virtual city are Utilize a texture image for the cognition of real object. In this study, building's facet images were achieved by a digital camera and adjusted its distortion by use of the 2D projective transformation method. After then, Images are mapped to a 3D building model by means of the OpenGL. Application program is able to offer an automation solution to construction process of the 3D virtual city.

• Bulletin of the Korean Mathematical Society
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• v.57 no.2
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• pp.419-427
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• 2020

In this paper, the projectivity of finitely generated flat modules of a commutative ring are studied from a topological point of view. Then various interesting results are obtained. For instance, it is shown that if a ring has either finitely many minimal primes or finitely many maximal ideals then every finitely generated flat module over it is projective. It is also shown that if a particular subset of the prime spectrum of a ring satisfies some certain ascending or descending chain conditions, then every finitely generated flat module over this ring is projective. These results generalize some major results in the literature on the projectivity of finitely generated flat modules.

• Proceedings of the KIEE Conference
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• 2006.07d
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• pp.1958-1959
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• 2006

This paper proposes a local path-planning algorithm that enables a mobile robot with vision sensor in a local area.The proposed method based on projective geometry and a wavefront method finds local-paths to avoid collisions using 3-D walls or obstacles map generated using projective geometry. Simulation results show the feasibility of the proposed method

• The Pure and Applied Mathematics
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• v.21 no.4
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• pp.257-270
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• 2014

In this article, we consider a homogeneous function of degree four in quaternionic vector spaces and $S^{4n+3}$ which is invariant under $S^3$ and U(n + 1)-action. We show it is an isoparametric function providing isoparametric hypersurfaces in $S^{4n+3}$ with g = 4 distinct principal curvatures and isoparametric hypersurfaces in quaternionic projective spaces with g = 5. This extends study of Nomizu on isoparametric function on complex vector spaces and complex projective spaces.

• The Pure and Applied Mathematics
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• v.23 no.4
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• pp.329-337
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• 2016

In this paper, we show that every compactification, which is a quasi-F space, of a space X is a Wallman compactification and that for any compactification K of the space X, the minimal quasi-F cover QFK of K is also a Wallman compactification of the inverse image ${\Phi}_K^{-1}(X)$ of the space X under the covering map ${\Phi}_K:QFK{\rightarrow}K$. Using these, we show that for any space X, ${\beta}QFX=QF{\beta}{\upsilon}X$ and that a realcompact space X is a projective object in the category $Rcomp_{\sharp}$ of all realcompact spaces and their $z^{\sharp}$-irreducible maps if and only if X is a quasi-F space.

• Korean Journal of Mathematics
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• v.21 no.4
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• pp.401-419
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• 2013

Let $n{\geq}0$ be an arbitrary integer. We define the class of almost n-simply presented abelian p-groups. It naturally strengthens all the notions of almost simply presented groups introduced by Hill and Ullery in Czechoslovak Math. J. (1996), n-simply presented p-groups defined by the present author and Keef in Houston J. Math. (2012), and almost ${\omega}_1-p^{{\omega}+n}$-projective groups developed by the same author in an upcoming publication [3]. Some comprehensive characterizations of the new concept are established such as Nunke-esque results as well as results on direct summands and ${\omega}_1$-bijections.