• The Pure and Applied Mathematics
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• v.13 no.3 s.33
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• pp.189-195
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• 2006

Let R be a prime ring with characteristics not 2 and ${\sigma},\;{\tau},\;{\alpha},\;{\beta}$ be auto-morphisms of R. Suppose that $d_1$ is a (${\sigma},\;{\tau}$)-derivation and $d_2$ is a (${\alpha},\;{\beta}$)-derivation on R such that $d_{2}{\alpha}\;=\;{\alpha}d_2,\;d_2{\beta}\;=\;{\beta}d_2$. In this note it is shown that; (1) If $d_1d_2$(R) = 0 then $d_1$ = 0 or $d_2$ = 0. (2) If [$d_1(R),d_2(R)$] = 0 then R is commutative. (3) If($d_1(R),d_2(R)$) = 0 then R is commutative. (4) If $[d_1(R),d_2(R)]_{\sigma,\tau}$ = 0 then R is commutative.

• Communications of the Korean Mathematical Society
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• v.36 no.2
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• pp.197-207
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• 2021

The main purpose of this paper is to study the zero-divisor properties of the zero-symmetric near-ring of skew formal power series R₀[[x; α]], where R is a symmetric, α-compatible and right Noetherian ring. It is shown that if R is reduced, then the set of all zero-divisor elements of R₀[[x; α]] forms an ideal of R₀[[x; α]] if and only if Z(R) is an ideal of R. Also, if R is a non-reduced ring and annR(a - b) ∩ Nil(R) ≠ 0 for each a, b ∈ Z(R), then Z(R₀[[x; α]]) is an ideal of R₀[[x; α]]. Moreover, if R is a non-reduced right Noetherian ring and Z(R₀[[x; α]]) forms an ideal, then ann_R(a - b) ∩ Nil(R) ≠ 0 for each a, b ∈ Z(R). Also, it is proved that the only possible diameters of the zero-divisor graph of R₀[[x; α]] is 2 and 3.

• Kyungpook Mathematical Journal
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• v.32 no.1
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• pp.21-30
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• 1992

• Korean Security Journal
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• no.16
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• pp.101-118
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• 2008

The subjects in this study were 500 students who were selected from a population that consisted of security majors who took courses in martial arts in four different four-year-course universities. After a survey was conducted, the answer sheets from 451 students were analyzed except 49 incomplete ones. The collected data were analyzed with SPSS Ver. 12.0 program. Frequency analysis, t-test and one-way ANOVA were utilized, and LSD and regression analysis were employed to make a post-hoc comparison. All the hypotheses formulated in this study were verified at the a=.05(Chronbach's alpha) level of significance. The findings of the study were as follows: First, as for relations between demographic characteristics and self- realization, the college students investigated were statistically different according to gender in three subvariables of self-realization that included ability development, ability display and attainment of ideal. Age and academic year made a significant difference to their ability development and attainment of ideal, and they differed statistically significantly in terms of ability development according to black lebel test. Second, concerning connections between the degree of martial-arts training and self-realization, training term, one of the subvariables of the degree of martial-arts training had a positive correlation to their ability development and attainment of ideal at the 5% level of significance, and training time was positively correlated to their ability development at the 5% level of significance. Third, training term, one of the subvariables of the degree of martial- arts training, had an impact on ability development, and that exerted a firsthand influence on attainment of ideal as well.

• Bulletin of the Korean Mathematical Society
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• v.30 no.2
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• pp.193-199
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• 1993

A hereditary $C^{*}$-subalgebra B of a $C^{*}$-algebra A is said to be full if B is not contained in any proper closed two-sided ideal in A, so each hereditary $C^{*}$-subalgebra of a simple $C^{*}$-algebra is always full. It is well known that every $C^{*}$-algebra is strong Morita equivalent to its full hereditary $C^{*}$-subalgebra, but the strong Morita equivalence of a $C^{*}$-algebra A and its hereditary $C^{*}$-subalgebra B does not imply the fullness of B, ingeneral. We present the following lemma for our computational convenience in the course of the proof of the main theorem. Note that $L_{B}$, $L_{B}$$^{*}$ and $L_{B}$ $L_{B}$$^{*}$ are all .alpha.-invariant whenever B is .alpha.-invariant under the action .alpha. of G.a. of G.a. of G.a. of G.f G.

• Journal of the Korean Mathematical Society
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• v.42 no.2
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• pp.203-222
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• 2005

Thompson series is a Hauptmodul for a genus zero group which lies between $\Gamma$o(N) and its normalizer in PSL2(R) ([1]). We construct explicit ring class fields over an imaginary quadratic field K from the Thompson series $T_g$($\alpha$) (Theorem 4), which would be an extension of [3], Theorem 3.7.5 (2) by using the Shimura theory and the standard results of complex multiplication. Also we construct various class fields over K, over a CM-field K (${\zeta}N + {\zeta}_N^{-1}$), and over a field K (${\zeta}N$). Furthermore, we find an explicit formula for the conjugates of Tg ($\alpha$) to calculate its minimal polynomial where $\alpha$ (${\in}{\eta}$) is the quotient of a basis of an integral ideal in K.

• Bulletin of the Korean Mathematical Society
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• v.54 no.4
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• pp.1331-1336
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• 2017

Assume that R is a commutative Noetherian ring with non-zero identity, a is an ideal of R, X is an R-module, and t is a non-negative integer. In this paper, we present upper bounds for the injective dimension of X in terms of the injective dimensions of its local cohomology modules and an upper bound for the injective dimension of $H^t_{\alpha}(X)$ in terms of the injective dimensions of the modules $H^i_{\alpha}(X)$, $i{\neq}t$, and that of X. As a consequence, we observe that R is Gorenstein whenever $H^t_{\alpha}(R)$ is of finite injective dimension for all i.

• Communications of the Korean Mathematical Society
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• v.39 no.2
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• pp.373-397
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• 2024

Lambek introduced the concept of symmetric rings to expand the commutative ideal theory to noncommutative rings. In this study, we propose an extension of symmetric rings called strongly α-symmetric rings, which serves as both a generalization of strongly symmetric rings and an extension of symmetric rings. We define a ring R as strongly α-symmetric if the skew polynomial ring R[x; α] is symmetric. Consequently, we provide proofs for previously established outcomes regarding symmetric and strongly symmetric rings, directly derived from the results we have obtained. Furthermore, we explore various properties and extensions of strongly α-symmetric rings.

• KIEE International Transactions on Electrophysics and Applications
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• v.4C no.3
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• pp.111-116
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• 2004

The Ni/SiC Schottky diode was fabricated with the $\alpha$-SiC thin film grown by the ICP-CVD method on a (111) Si wafer. $\alpha$-SiC film has been grown on a carbonized Si layer in which the Si surface was chemically converted to a very thin SiC layer achieved using an ICP-CVD method at $700^{\circ}C$. To reduce defects between the Si and $\alpha$-SiC, the surface of the Si wafer was slightly carbonized. The film characteristics of $\alpha$-SiC were investigated by employing TEM (Transmission Electron Microscopy) and FT-IR (Fourier Transform Infrared Spectroscopy). Sputterd Ni thin film was used as the anode metal. The boundary status of the Ni/SiC contact was investigated by AES (Auger Electron Spectroscopy) as a function of the annealing temperature. It is shown that the ohmic contact could be acquired beyond a 100$0^{\circ}C$ annealing temperature. The forward voltage drop at 100A/cm was I.0V. The breakdown voltage of the Ni/$\alpha$-SiC Schottky diode was 545 V, which is five times larger than the ideal breakdown voltage of the silicon device. As well, the dependence of barrier height on temperature was observed. The barrier height from C- V characteristics was higher than those from I-V.

• Kyungpook Mathematical Journal
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• v.55 no.4
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• pp.827-835
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• 2015

Let U be a ${\sigma}$-square closed Lie ideal of a 2-torsion free ${\sigma}$-prime ${\Gamma}$-ring M. Let $d{\neq}1$ be an automorphism of M such that $[u,d(u)]_{\alpha}{\in}Z(M)$ on U, $d{\sigma}={\sigma}d$ on U, and there exists $u_0$ in $Sa_{\sigma}(M)$ with $M{\Gamma}u_0{\subseteq}U$. Then, $U{\subseteq}Z(M)$. By applying this result, we generalize the results of Oukhtite and Salhi respect to ${\Gamma}$-rings. Finally, for a non-zero derivation of a 2-torsion free ${\sigma}$-prime $\Gamma$-ring, we obtain suitable conditions under which the $\Gamma$-ring must be commutative.