• Communications of the Korean Mathematical Society
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• v.27 no.3
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• pp.483-488
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• 2012

In this paper we introduce the notion of P-strongly regular near-ring. We have shown that a zero-symmetric near-ring N is P-strongly regular if and only if N is P-regular and P is a completely semiprime ideal. We have also shown that in a P-strongly regular near-ring N, the following holds: (i) $Na$ + P is an ideal of N for any $a{\in}N$. (ii) Every P-prime ideal of N containing P is maximal. (iii) Every ideal I of N fulfills I + P = $I^2$ + P.

• Bulletin of the Korean Mathematical Society
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• v.39 no.4
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• pp.645-652
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• 2002

In this note we investigate some results which concern the types of local rings. In particular it is shown that if the type of a quasi-unmixed local ring A is less than or equal to depth A ＋ 1, and $\hat{A}_p$ is Cohen-Macaulay for every prime $p\neq\hat{m}$, then A is Cohen-Macaulay. (This implies the previously known result: if A satisfies $(S_{n-1})}$, where n is the type of a .ins A, then A is Cohen-Macaulay.)

• Bulletin of the Korean Mathematical Society
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• v.43 no.2
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• pp.299-307
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• 2006

The following results ale extended from P-injective rings to AP-injective rings: (1) R is left self-injective regular if and only if R is a right (resp. left) AP-injective ring such that for every finitely generated left R-module M, $_R(M/Z(M))$ is projective, where Z(M) is the left singular submodule of $_{R}M$; (2) if R is a left nonsingular left AP-injective ring such that every maximal left ideal of R is either injective or a two-sided ideal of R, then R is either left self-injective regular or strongly regular. In addition, we answer a question of Roger Yue Chi Ming [13] in the positive. Let R be a ring whose every simple singular left R-module is Y J-injective. If R is a right MI-ring whose every essential right ideal is an essential left ideal, then R is a left and right self-injective regular, left and right V-ring of bounded index.

• Communications of the Korean Mathematical Society
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• v.17 no.2
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• pp.221-227
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• 2002

In this paper we will show that the followings ; (1) Let R be a regular local ring of dimension n. Then $A_{n-2}$(R) = 0. (2) Let R be a regular local ring of dimension n and I be an ideal in R of height 3 such that R/I is a Gorenstein ring. Then [I] = 0 in $A_{n-3}$(R). (3) Let R = V[[ $X_1$, $X_2$, …, $X_{5}$ ]]/(p+ $X_1$$^{t1}$ + $X_2$$^{t2}$ + $X_3$$^{t3}$ + $X_4$$^2$+ $X_{5}$ $^2$/), where p $\neq$2, $t_1$, $t_2$, $t_3$ are arbitrary positive integers and V is a complete discrete valuation ring with (p) = mv. Assume that R/m is algebraically closed. Then all the Chow group for R is 0 except the last Chow group.group.oup.

• Korean Journal of Environmental Agriculture
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• v.30 no.3
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• pp.229-233
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• 2011

BACKGROUND: Soil acidification, which is known to be one of the reasons of forest decline, is associated with decreases in exchangeable Ca and increases in Al concentration, leading to low Ca/Al ratio in soil solution. As tree rings are datable archives of environmental changes, Ca/Al ratios of annual growth ring may show decreasing pattern in accordance with the progress of soil acidification. This study was conducted to investigate Ca/Al pattern of Pinus densiflora tree ring in an attempt to test its usefulness as an indicator of historical soil acidification. METHODS AND RESULTS: Three P. densiflora tree disks were collected from P. densiflora forests in Jeonnam province, and soil samples (0-10, 10-20, and 20-30 cm in depth) were also collected from the tree locations. Soils were analyzed for pH and exchangeable Ca and Al concentrations, and Ca/Al was calculated. Annual growth rings formed between 1969 and 2007 were separated and analyzed for Ca/Al. Soil Ca/Al was positively (P<0.01) correlated with soil pH, suggesting that soil acidification decreased Ca while increasing Al availability, lowering Ca/Al in soil solution. The Ca/Al of tree rings also showed a decreasing pattern from 18.2 to 5.5 during the period, and this seemed to reflect historical acidification of the soils. CONCLUSION(s): The relationship between soil pH and Ca/Al and the decreasing pattern of Ca/Al of tree ring suggest that Ca/Al of tree ring needs to be considered as a proxy of the progress of soil acidification in P. densiflora forest in southern Korea.

• The Transactions of the Korean Institute of Electrical Engineers C
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• v.51 no.3
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• pp.99-104
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• 2002

lateral insulated gate bipolar transistors(LIGBTs) are extensively used in high voltage power IC application due to their low forward voltage drops. One of the main disadvantages of the LIGBT is its scow switching speed when compared to the LDMOSFET. And the LIGBT with reverse channel structure is lower current capability than the conventional LIGBT at the forward conduction mode. In this paper, the LIGBT which included p+ ring and p-channel gate is presented at the reverie channel structure. The presented LIGBT structure is proposed to suppress the latch up, efficiently and to improve the turn off time. It is shown to improve the current capability too. It is verified 2-D simulator, MEDICI. It is shown that the latch up current of new LIGBT is 10 times than that of the conventional LIGBT Additionally, it is shown that the turn off characteristics of the proposed LIGBT is i times than that of the conventional LIGBT. It is net presented the tail current of turn off characteristics at the proposed structure. And the presented LIGBT is not n+ buffer layer because it includes p channel gate and p+ ring.

• Bulletin of the Korean Mathematical Society
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• v.55 no.6
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• pp.1627-1638
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• 2018

In this paper, we study an special type of cyclic codes called skew cyclic codes over the ring ${\mathbb{F}}_p+v{\mathbb{F}}_p+v^2{\mathbb{F}}_p$, where p is a prime number. This set of codes are the result of module (or ring) structure of the skew polynomial ring (${\mathbb{F}}_p+v{\mathbb{F}}_p+v^2{\mathbb{F}}_p$)[$x;{\theta}$] where $v^3=1$ and ${\theta}$ is an ${\mathbb{F}}_p$-automorphism such that ${\theta}(v)=v^2$. We show that when n is even, these codes are either principal or generated by two elements. The generator and parity check matrix are proposed. Some examples of linear codes with optimum Hamming distance are also provided.

• Kyungpook Mathematical Journal
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• v.46 no.1
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• pp.57-64
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• 2006

It is proved that if G is a direct sum of countable abelian $p$-groups and R is a special selected commutative unitary highly-generated ring of prime characteristic $p$, which ring is more general than the weakly perfect one, then the group of all normed units V (RG) modulo G, that is V (RG)=G, is a direct sum of countable groups as well. This strengthens a result due to W. May, published in (Proc. Amer. Math. Soc., 1979), that treats the same question but over a perfect ring.

• East Asian mathematical journal
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• v.38 no.1
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• pp.1-12
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• 2022

Let R be a ring with an endomorphism σ and a σ-derivation δ. R is called (σ, δ)-Baer (resp. (σ, δ)-quasi-Baer, (σ, δ)-p.q.-Baer, (σ, δ)-p.p.) if the right annihilator of every right (σ, δ)-set (resp., (σ, δ)-ideal, principal (σ, δ)-ideal, (σ, δ)-element) of R is generated by an idempotent of R. In this paper, for a given Ore extension A = R[x; σ, δ] of R, the following properties are investigated: If R is a σ-rigid ring in which σ and δ commute, then (1) R is (σ, δ)-Baer if and only if R is (σ, δ)-quasi-Baer if and only if A is (${\bar{\sigma}},\;{\bar{\delta}}$)-Baer if and only if A is (${\bar{\sigma}},\;{\bar{\delta}}$)-quasi-Baer; (2) R is (σ, δ)-p.p. if and only if R is (σ, δ)-p.q.-Baer if and only if A is (${\bar{\sigma}},\;{\bar{\delta}}$)-p.p. if and only if A is (${\bar{\sigma}},\;{\bar{\delta}}$)-p.q.-Baer.

• Bulletin of the Korean Chemical Society
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• v.18 no.6
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• pp.657-662
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• 1997

Gas-phase phenyl group migration within the protonated ketones has been studied MO theoretically using the AM1 method. The initial state structure shows relatively strong resonance delocalization of positive charge into the nonmigrating (Y) ring, while the ring migration (Z-ring) is nearly complete in the transition state. These results are reflected in the large $p^+_Z$ (<0) and $p^+_$Y (>0) values and in the predominant contribution of resonance (r) over inductive (field, f) effect, r/f ranging from 1.3 ($p^+_r$) to 1.5 ($p^+_z$). The cross-interaction constant $p_{YZ}$ is vanishingly small ($p_{YZ}$=0.03) which is in contrast to the larger magnitudes for benzilic ($p_{YZ}$=-0.48) and azibenzil ($p_{YZ}$=-0.53) rearrangement processes. The relationship found between the extent of resonance contribution in the initial state and the magnitude of $p_{YZ}$ provides strong support for the proportionality between the magnitude of $p_{YZ}$ and the change in the intensity of interaction, ${\Delta}I^{\cdot}_{YZ}$, in the activation process.