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Korean Journal of Mathematics
Journal Basic Information
pISSN :
1976-8605
eISSN :
2288-1433
Journal DOI :
10.11568/kjm
Frequency :
Others
Publisher:
The Kangwon-Kyungki Mathematical Society
Editor in Chief :
Volume & Issues
Volume 20, Issue 4 - Dec 2012
Volume 20, Issue 3 - Sep 2012
Volume 20, Issue 2 - Jun 2012
Volume 20, Issue 1 - Mar 2012
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1
RINGS OVER WHICH POLYNOMIAL RINGS ARE ARMENDARIZ AND REVERSIBLE
Ahn, Jung Ho ; Choi, Min Jeong ; Choi, Si Ra ; Jeong, Won Seok ; Kim, Jung Soo ; Lee, Jeong Yeol ; Lee, Soon Ji ; Lee, Young Sun ; Noh, Dong Hyun ; Noh, Yu Seung ; Park, Gyeong Hyeon ; Lee, Chang Ik ; Lee, Yang ;
Korean Journal of Mathematics, volume 20, issue 3, 2012, Pages 273~284
DOI : 10.11568/kjm.2012.20.3.273
Abstract
A ring R is called reversibly Armendariz if
for all
,
whenever
for two polynomials
over R. It is proved that a ring R is reversibly Armendariz if and only if its polynomial ring is reversibly Armendariz if and only if its Laurent polynomial ring is reversibly Armendariz. Relations between reversibly Armendariz rings and related ring properties are examined in this note, observing the structures of many examples concerned. Various kinds of reversibly Armendariz rings are provided in the process. Especially it is shown to be possible to construct reversibly Armendariz rings from given any Armendariz rings.
2
DETERMINANT AND SPECTRUM PRESERVING MAPS ON M
_{n}
Kim, Sang Og ;
Korean Journal of Mathematics, volume 20, issue 3, 2012, Pages 285~291
DOI : 10.11568/kjm.2012.20.3.285
Abstract
Let
be the algebra of all complex
matrices and
a surjective map (not necessarily additive or multiplicative) satisfying one of the following equations:
. Then it is an automorphism, where
is the spectrum of
. We also show that if
be a standard operator algebra,
is a unital Banach algebra with trivial center and if
is a multiplicative surjection preserving spectrum, then
is an algebra isomorphism.
3
MODAL, NECESSITY, SUFFICIENCY AND CO-SUFFICIENCY OPERATORS
Kim, Yong Chan ;
Korean Journal of Mathematics, volume 20, issue 3, 2012, Pages 293~305
DOI : 10.11568/kjm.2012.20.3.293
Abstract
We investigate the properties of modal, necessity, sufficiency and co-sufficiency operators. We show that their operations induce various relations, respectively.
4
PROPERTIES OF INDUCED INVERSE POLYNOMIAL MODULES OVER A SUBMONOID
Cho, Eunha ; Jeong, Jinsun ;
Korean Journal of Mathematics, volume 20, issue 3, 2012, Pages 307~314
DOI : 10.11568/kjm.2012.20.3.307
Abstract
Let M be a left R-module and R be a ring with unity, and
be a submonoid. Then
is an
-module. In this paper we show some properties of
as an
-module. Let
be an R-linear map and
and define
. Then
is an
-module. We show that given a short exact sequence
of R-modules,
is a short exact sequence of
-module. Then we show
is not an injective left
-module, in general.
5
SOME PROPERTIES OF GR-MULTIPLICATION MODULES
Park, Seungkook ;
Korean Journal of Mathematics, volume 20, issue 3, 2012, Pages 315~321
DOI : 10.11568/kjm.2012.20.3.315
Abstract
In this paper, we provide the necessary and sufficient conditions for a faithful graded module to be a graded multiplication module and for a graded submodule of a faithful gr-multiplication to be gr-essential.
6
A HIGH-ORDER MODEL FOR SPIKE AND BUBBLE IN IMPULSIVELY ACCELERATED INTERFACE
Sohn, Sung-Ik ;
Korean Journal of Mathematics, volume 20, issue 3, 2012, Pages 323~331
DOI : 10.11568/kjm.2012.20.3.323
Abstract
We present a high-order potential ow model for the motion of the impulsively accelerated unstable interface of infinite density jump. The Layzer model for the evolution of the interface is extended to high-order. The time-evolution solutions of the bubble and the spike in the interface are obtained from the high-order model. We show that the high-order model gives improvement on the prediction of the evolution of the bubble and the spike.
7
BIFURCATION PROBLEM FOR THE SUPERLINEAR ELLIPTIC OPERATOR
Jung, Tacksun ; Choi, Q-Heung ;
Korean Journal of Mathematics, volume 20, issue 3, 2012, Pages 333~341
DOI : 10.11568/kjm.2012.20.3.333
Abstract
We investigate the number of solutions for the superlinear elliptic bifurcation problem with Dirichlet boundary condition. We get a theorem which shows the existence of at least
weak solutions for the superlinear elliptic bifurcation problem with boundary value condition. We obtain this result by using the critical point theory induced from invariant linear subspace and the invariant functional.
8
PROJECTIVE REPRESENTATIONS OF A QUIVER WITH THREE VERTICES AND TWO EDGES AS R[x]-MODULES
Han, Juncheol ; Park, Sangwon ;
Korean Journal of Mathematics, volume 20, issue 3, 2012, Pages 343~352
DOI : 10.11568/kjm.2012.20.3.343
Abstract
In this paper we show that the projective properties of representations of a quiver
as left
-modules. We show that if P is a projective left R-module then
is a projective representation of a quiver Q as
-modules, but
is not a projective representation of a quiver Q as
-modules, if
. And we show a representation
of a quiver Q is a projective representation, if P is a projective left R-module, but
is not a projective representation of a quiver Q as
-modules, if
. Then we show a representation
of a quiver Q is a projective representation, if P is a projective left R-module.
9
GENERALIZED FIXED POINT THEOREMS IN CONE METRIC SPACES
Kim, Seung Hyun ; Lee, Byung Soo ;
Korean Journal of Mathematics, volume 20, issue 3, 2012, Pages 353~360
DOI : 10.11568/kjm.2012.20.3.353
Abstract
In this paper we introduce the property (C), which is a cone metric extension of the usual metric property (E,A) and consider fixed point theorems for generalized contractive mappings under suitable conditions in cone metric spaces without normal cones.
10
SIX SOLUTIONS FOR THE SEMILINEAR WAVE EQUATION WITH NONLINEARITY CROSSING THREE EIGENVALUES
Choi, Q-Heung ; Jung, Tacksun ;
Korean Journal of Mathematics, volume 20, issue 3, 2012, Pages 361~369
DOI : 10.11568/kjm.2012.20.3.361
Abstract
We get a theorem which shows the existence of at least six solutions for the semilinear wave equation with nonlinearity crossing three eigenvalues. We obtain this result by the variational reduction method and the geometric mapping defined on the finite dimensional subspace. We use a contraction mapping principle to reduce the problem on the infinite dimensional space to that on the finite dimensional subspace. We construct a three-dimensional subspace with three axes spanned by three eigenvalues and a mapping from the finite dimensional subspace to the one-dimensional subspace.