• East Asian mathematical journal
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• v.16 no.1
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• pp.111-123
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• 2000

Northcott and McKerrow proved that if R is a left noetherian ring and E is an injective left R-module, then $E[x^{-1}]$ is an injective left R[xl-module. Park generalize Northcott and McKerrow's result so that if R is a left noetherian ring and E is an injective left R-module, then $E[x^{-S}]$ is an injective left $R[x^s]$-module, where S is a submonoid of N(N is the set of all natural numbers). In this paper we show $$Hom_{R[x^S]}(M[x^{-S}],\;N[x^{-S}]){\cong}Hom_R(M,\;N)[[x^S]]$$ and using the above result and this isomorphism, finally we show that $$Ext^i_{R[x^S]}(M[x^{-S}],\;N[x^{-S}]){\cong}Ext^i_R(M,\;N)[[x^S]]$$.

• Journal of the Korean Mathematical Society
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• v.52 no.3
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• pp.489-501
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• 2015

We study the structure of right duo ring property when it is restricted within the group of units, and introduce the concept of right unit-duo. This newly introduced property is first observed to be not left-right symmetric, and we examine several conditions to ensure the symmetry. Right unit-duo rings are next proved to be Abelian, by help of which the class of noncommutative right unit-duo rings of minimal order is completely determined up to isomorphism. We also investigate some properties of right unit-duo rings which are concerned with annihilating conditions.

• Honam Mathematical Journal
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• v.31 no.3
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• pp.279-292
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• 2009

As a survey-type article, the paper reviews some results on a regular covering space in digital covering theory. The recent paper [10](see also [12]) established the notion of regular covering space in digital covering theory and studied its various properties. Besides, the papers [14, 16] developed a discrete Deck's transformation group of a digital covering. In this paper we study further their properties. By using these properties, we can classify digital covering spaces. Finally, the paper proposes an open problem.

• Honam Mathematical Journal
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• v.31 no.3
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• pp.267-278
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• 2009

As a survey-type article, the paper reviews the recent results on a (generalized) universal covering space in digital covering theory. The recent paper [19] established the generalized universal (2, k)-covering property which improves the universal (2, k)-covering property of [3]. In algebraic topology it is well-known that a simply connected and locally path connected covering space is a universal covering space. Unlike this property, in digital covering theory we can propose that a generalized universal covering space has its intrinsic feature. This property can be useful in classifying digital covering spaces and in studying a shortest k-path problem in data structure.

• Journal of the Chungcheong Mathematical Society
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• v.10 no.1
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• pp.43-56
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• 1997

In this paper, we introduce a new class of ${\delta}$-frames and study its properties. To do so, we introduce ${\delta}$-filters, almost Lindel$\ddot{o}$f frames and Lindel$\ddot{o}$f frames. First, we show that a complete chain or a complete Boolean algebra is a ${\delta}$-frame. Next, we show that a ${\delta}$-frame L is almost Lindel$\ddot{o}$f iff for any ${\delta}$-filter F in L, ${\vee}\{x^*\;:\;x{\in}F\}{\neq}e$. Last, we show that every regular Lindelof ${\delta}$-frame is normal and a Lindel$\ddot{o}$f ${\delta}$-frame is preserved under a ${\delta}$-isomorphism which is dense and codense.

• Honam Mathematical Journal
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• v.36 no.1
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• pp.199-215
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• 2014

Owing to the development of the notion of normal adjacency of a digital product [9], product properties of digital topological properties were studied efficiently. To equivalently represent a normal adjacency of a digital product, the present paper proposes an S-compatible adjacency of a digital product. This approach can be helpful to understand a normal adjacency of a digital product. Finally, using an S-compatible adjacency of a digital product, we can study product properties of digital topological properties, which improves the presentations of the normal adjacency of a digital product in [9] and [5, 6].

• Bulletin of the Korean Mathematical Society
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• v.52 no.4
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• pp.1297-1303
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• 2015

We study Samelson products on models of function spaces. Given a map $f:X{\rightarrow}Y$ between 1-connected spaces and its Quillen model ${\mathbb{L}}(f):{\mathbb{L}}(V){\rightarrow}{\mathbb{L}}(W)$, there is an isomorphism of graded vector spaces ${\Theta}:H_*(Hom_{TV}(TV{\otimes}({\mathbb{Q}}{\oplus}sV),{\mathbb{L}}(W))){\rightarrow}H_*({\mathbb{L}}(W){\oplus}Der({\mathbb{L}}(V),{\mathbb{L}}(W)))$. We define a Samelson product on $H_*(Hom_{TV}(TV{\otimes}({\mathbb{Q}}{\oplus}sV),{\mathbb{L}}(W)))$.

• Journal of the Korean Institute of Telematics and Electronics
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• v.17 no.3
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• pp.1-11
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• 1980

For an ordinary engineer or researcher there are too diversified branches or even disciplines which have their own jargon to complicate an easy access, Nevertheless in many cases an isomorphism or even identity of notions exist to escape our grasp when expressed in different discipline or context, In this paper the masterwork of Box and Jenkins is introduced to accustom a few terms of statisticiens, to be followed by the technique of smoothing filtering of Wiener and Kalman - Bucy. The advantages of a transform (for example Hadamard) technique are explaned as well as authors personal philosophical views.

• Communications of the Korean Mathematical Society
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• v.12 no.3
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• pp.631-643
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• 1997

In this paper, we introduce (4k-1)-diagonal algebras $Alg{\iota}(\array{4k-a\\2n}\)$ AND $Alg{\iota}(\array{4k-a\\2n+1}\)$ and investigate necessary and sufficient conditions that isomorphisms of $Alg{\iota}(\array{4k-a\\2n}\)$ AND $Alg{\iota}(\array{4k-a\\2n+1}\)$ are spatially implemented.

• Honam Mathematical Journal
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• v.32 no.1
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• pp.45-51
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• 2010

Let A be an abelian variety defined over a number field K and let L be a cyclic extension of K with Galois group G = <${\sigma}$> of order n. Let III(A/K) and III(A/L) denote, respectively, the Tate-Shafarevich groups of A over K and of A over L. Assume III(A/L) is finite. Let M(x) be a companion matrix of 1+x+${\cdots}$+$x^{n-1}$ and let $A^x$ be the twist of $A^{n-1}$ defined by $f^{-1}{\circ}f^{\sigma}$ = M(x) where $f:A^{n-1}{\rightarrow}A^x$ is an isomorphism defined over L. In this paper we compute [III(A/K)][III($A^x$/K)]/[III(A/L)] in terms of cohomology, where [X] is the order of an finite abelian group X.