• Communications of the Korean Mathematical Society
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• v.38 no.1
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• pp.39-46
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• 2023

Let R be a commutative ring, M be a Noetherian R-module, and N a 2-absorbing submodule of M such that r(N :_R M) = 𝖕 is a prime ideal of R. The main result of the paper states that if N = Q₁ ∩ ⋯ ∩ Q_n with r(Q_i :_R M) = 𝖕_i, for i = 1, . . . , n, is a minimal primary decomposition of N, then the following statements are true. (i) 𝖕 = 𝖕_k for some 1 ≤ k ≤ n. (ii) For each j = 1, . . . , n there exists m_j ∈ M such that 𝖕_j = (N :_R m_j). (iii) For each i, j = 1, . . . , n either 𝖕_i ⊆ 𝖕_j or 𝖕_j ⊆ 𝖕_i. Let Γ_E(M) denote the zero-divisor graph of equivalence classes of zero divisors of M. It is shown that {Q₁∩ ⋯ ∩Q_n-1, Q₁∩ ⋯ ∩Q_n-2, . . . , Q₁} is an independent subset of V (Γ_E(M)), whenever the zero submodule of M is a 2-absorbing submodule and Q₁ ∩ ⋯ ∩ Q_n = 0 is its minimal primary decomposition. Furthermore, it is proved that Γ_E(M)[(0 :_R M)], the induced subgraph of Γ_E(M) by (0 :_R M), is complete.

• Proceedings of the KIEE Conference
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• 2007.04c
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• pp.156-158
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• 2007

Laser wave length can have evaporation effect by absorption because outer skin or tissue of focus is consisted of water almost though absorption of water occurs more than 90% almost in formation thickness of very thin floor Can operate outer skin, steam by floor and correct incision of formation is available. Suture surgical operation is avaliable to vein or lymph system and surgical operation region can dry and see as eye and radish bleeding surgical operation is avaliable Specially, stability of tube both end output about pulse by weight very, this research can cause various curative effect because can reduce bulk and control easily current wave style of medical laser using electric power conversion device of high frequency way. If introduce ZVS (Zero Voltage Switching) or ZVZCS (Zero Voltage and Zero Current Switching), is more profitable because can reduce switching damage Because electric power department of proposed medical laser can do stable soft-switching in wide subordinate extent introducing ZVZCS technique by the first help and control department composes microcontroller, output current waveform user have free form make. Result that experiment because design and manufacture, brought result that improve of 20% than existing equipment, and will be bought to get into superior result if supplement as systematic late.

• Proceedings of the KIEE Conference
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• 2007.04a
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• pp.52-54
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• 2007

Laser wave length can have evaporation effect by absorption because outer skin or tissue of focus is consisted of water almost though absorption of water occurs more than 90% almost in formation thickness of very thin floor. Can operate outer skin, steam by floor and correct incision of formation is available. Suture surgical operation is available to vein or lymph system and surgical operation region can dry and see as eye and radish bleeding surgical operation is available. Specially, stability of tube both end output about pulse by weight very, this research can cause various curative effect because can reduce bulk and control easily current wave style of medical laser using electric power conversion device of high frequency way. If introduce ZVS (Zero Voltage Switching) or ZVZCS (Zero Voltage and Zero Current Switching), is more profitable because can reduce switching damage. Because electric power department of proposed medical laser can do stable soft-switching in wide subordinate extent introducing ZVZCS technique by the first help and control department composes microcontroller, output current waveform user have free form make. Result that experiment because design and manufacture, brought result that improve of 20% than existing equipment, and will be bought to get into superior result if supplement as systematic late.

• Journal of the Korean Mathematical Society
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• v.34 no.4
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• pp.1009-1018
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• 1997

Observing that for any $\beta_c$-Wallman functor $A$ and any Tychonoff space X, there is a cover $(C_1(A(X), X), c_1)$ of X such that X is $A$-disconnected if and only if $c_1 : C_1(A(X), X) \longrightarrow X$ is a homeomorphism, we show that every Tychonoff space has the minimal $A$-disconnected cover. We also show that if X is weakly Lindelof or locally compact zero-dimensional space, then the minimal G-disconnected (equivalently, cloz)-cover is given by the space $C_1(A(X), X)$ which is a dense subspace of $E_cc(\betaX)$.

• Korean Journal of Mathematics
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• v.10 no.1
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• pp.45-51
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• 2002

Observing that a realcompactification Y of a space X is Wallman if and only if for any non-empty zero-set Z in Y, $Z{\cap}Y{\neq}{\emptyset}$, we will show that for any pseudo-Lindel$\ddot{o}$f space X, the minimal quasi-F $QF({\upsilon}X)$ of ${\upsilon}X$ is Wallman and that if X is weakly Lindel$\ddot{o}$, then $QF({\upsilon}X)={\upsilon}QF(X)$.

• Bulletin of the Korean Mathematical Society
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• v.40 no.1
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• pp.91-99
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• 2003

In this paper, we show that if the ring of a Merits context (A, B, M, N, ${\psi},\;{\phi}$) with zero pairings is a strongly $\pi$-regular ring of bounded index if and only if so are A and B. Furthermore, we extend this result to the ring of a Merits context over quasi-duo strongly $\pi$-regular rings.

• Bulletin of the Korean Mathematical Society
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• v.48 no.6
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• pp.1235-1243
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• 2011

In this paper, we investigate sharing value problems related to a meromorphic function f(z) and f(qz), where q is a non-zero constant. It is shown, for instance, that if f(z) is zero-order and shares two valves CM and one value IM with f(qz), then f(z) = f(qz).

• Bulletin of the Korean Mathematical Society
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• v.57 no.4
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• pp.865-872
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• 2020

Let X ⊂ ℙ^r be an integral and non-degenerate variety. Set n := dim(X). Let 𝜌(X)" be the maximal integer such that every zero-dimensional scheme Z ⊂ X smoothable in X is linearly independent. We prove that X is linearly normal if 𝜌(X)" ≥ 2⌈(r + 2)/2⌉ and that 𝜌(X)" < 2⌈(r + 1)/(n + 1)⌉, unless either n = r or X is a rational normal curve.

• Communications of the Korean Mathematical Society
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• v.17 no.2
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• pp.229-235
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• 2002

In this paper we show that if K is an incline with multiplicative identity and I is an r-ideal of k containing a unit u, then I = K. Moreover, we show that in a non-zero incline K with multiplicative identity and zero element, every proper r-ideal in K is contained in a maximal r-ideal of K.

• Honam Mathematical Journal
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• v.11 no.1
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• pp.15-19
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• 1989

A conjecture of E. T. H. Wang asserts that if every diagonal disjoint from m mutually disjoint zero diagonals of $A{\in}{\Omega}_n$ has a constant sum, then all entries off the m zero diagonals are equal to l/(n-m). E. T. H. Wang proved the conjecture for m=0, 1, n-2 and n-1. In the present paper, it is proved that the conjecture holds true for m=2.