• Journal of the Korean Mathematical Society
• /
• v.13 no.1
• /
• pp.133-139
• /
• 1976

• Journal of the Korean Mathematical Society
• /
• v.55 no.5
• /
• pp.1221-1233
• /
• 2018

Let R be a commutative ring with non-zero identity and let NN(R) = {I | I is a nonnil ideal of R}. Let M be an R-module and let ${\phi}-tor(M)=\{x{\in}M{\mid}Ix=0\text{ for some }I{\in}NN(R)\}$. If ${\phi}or(M)=M$, then M is called a ${\phi}$-torsion module. An R-module M is said to be ${\phi}$-flat, if $0{\rightarrow}{A{\otimes}_R}\;{M{\rightarrow}B{\otimes}_R}\;{M{\rightarrow}C{\otimes}_R}\;M{\rightarrow}0$ is an exact R-sequence, for any exact sequence of R-modules $0{\rightarrow}A{\rightarrow}B{\rightarrow}C{\rightarrow}0$, where C is ${\phi}$-torsion. In this paper, the concepts of NRD-submodules and NP-submodules are introduced, and the ${\phi}$-flat modules over a ${\phi}-Pr{\ddot{u}}fer$ ring are investigated.

• Journal of the Korean Statistical Society
• /
• v.35 no.4
• /
• pp.453-458
• /
• 2006

It is well known fact for the iid data that the limiting standard errors of sample autocorrelations are all unity for all time lags and they are asymptotically independent for different lags (Brockwell and Davis, 1991). It is also usual practice in time series modeling that this fact continues to be valid for white noise series which is a sequence of uncorrelated random variables. This paper contradicts this usual practice for white noise. We consider a sequence of martingale differences which belongs to white noise time series and derive exact joint asymptotic distributions of sample autocorrelations. Some implications of the result are illustrated for conditionally heteroscedastic time series.

• Journal of the Korean Mathematical Society
• /
• v.53 no.1
• /
• pp.1-17
• /
• 2016

Let $\mathcal{W}$ be an additive full subcategory of the category R-Mod of left R-modules. We provide a method to construct a proper ${\mathcal{W}}^H_C$-resolution (resp. coproper ${\mathcal{W}}^T_C$-coresolution) of one term in a short exact sequence in R-Mod from those of the other two terms. By using these constructions, we introduce and study the stability of the Gorenstein categories ${\mathcal{G}}_C({\mathcal{W}}{\mathcal{W}}^T_C)$ and ${\mathcal{G}}_C({\mathcal{W}}^H_C{\mathcal{W}})$ with respect to a semidualizing bimodule C, and investigate the 2-out-of-3 property of these categories of a short exact sequence by using these constructions. Also we prove how they are related to the Gorenstein categories ${\mathcal{G}}((R{\ltimes}C){\otimes}_R{\mathcal{W}})_C$ and ${\mathcal{G}}(Hom_R(R{\ltimes}C,{\mathcal{W}}))_C$ over $R{\ltimes}C$.

• Journal of the Korean Mathematical Society
• /
• v.43 no.3
• /
• pp.491-506
• /
• 2006

In this paper, we extend the concept of the group ${\varepsilon}(X)$ of self homotopy equivalences of a space X to that of an object in the category of pairs. Mainly, we study the group ${\varepsilon}(X,\;A)$ of pair homotopy equivalences from a CW-pair (X, A) to itself which is the special case of the extended concept. For a CW-pair (X, A), we find an exact sequence $1\;{\to}\;G\;{\to}\;{\varepsilon}(X,\;A)\;{to}\;{\varepsilon}(A)$ where G is a subgroup of ${\varepsilon}(X,\;A)$. Especially, for CW homotopy associative and inversive H-spaces X and Y, we obtain a split short exact sequence $1\;{\to}\;{\varepsilon}(X)\;{\to}\;{\varepsilon}(X{\times}Y,Y)\;{\to}\;{\varepsilon}(Y)\;{\to}\;1$ provided the two sets $[X{\wedge}Y,\;X{\times}Y]$ and [X, Y] are trivial.

• Bulletin of the Korean Mathematical Society
• /
• v.36 no.4
• /
• pp.661-669
• /
• 1999

L. Degui introduced an upper bound of Reidemeister number. In this paper we give a simple proof of Degui's Theorem.

• Communications of the Korean Mathematical Society
• /
• v.6 no.2
• /
• pp.193-202
• /
• 1991

• Journal of applied mathematics & informatics
• /
• v.3 no.1
• /
• pp.79-88
• /
• 1996

In this paper we define a new short exact sequence of automata and we investigate module-like properties on projective and injective automata

• Journal of the Korean Mathematical Society
• /
• v.54 no.5
• /
• pp.1623-1639
• /
• 2017

The generalized coGottlieb sets are not known to be groups in general. We study some conditions which make them groups. Moreover, there are actions on the generalized coGottlieb sets which are different from known actions up to now. We give related exact sequence of the generalized coGottlieb sets. Using them, we obtain certain results related to the maps which preserve generalized coGottlieb sets.

• Journal of the Korean Institute of Intelligent Systems
• /
• v.21 no.4
• /
• pp.506-511
• /
• 2011

In this paper we investigate some situations in connection with two exact sequences of fuzzy linear maps. Also we obtain a generalization of the work [Theorem4] of Pan [5], and we study the analogies of The Four Lemma and The Five Lemma of homological algebra. Finally we obtain a special exact sequence.