• Korean Journal of Mathematics
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• v.31 no.1
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• pp.95-107
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• 2023

Consider ℛ to be an associative prime ring and 𝒦 to be a nonzero dense ideal of ℛ. A mapping (need not be additive) ℱ : ℛ → 𝒬_mr associated with derivation d : ℛ → ℛ is called a multiplicative b-generalized derivation if ℱ(αδ) = ℱ(α)δ +bαd(δ) holds for all α, δ ∈ ℛ and for any fixed (0 ≠)b ∈ 𝒬_s ⊆ 𝒬_mr. In this manuscript, we study the commutativity of prime rings when the map b-generalized derivation satisfies the strong commutativity preserving condition and moreover, we investigate the commutativity of prime rings that admit multiplicative b-generalized derivation, which improves many results in the literature.

• Kyungpook Mathematical Journal
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• v.62 no.1
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• pp.43-55
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• 2022

Let R be a *-ring and n ≥ 1 be an integer. The objective of this paper is to introduce the notion of n-skew centralizing maps on *-rings, and investigate the impact of these maps. In particular, we describe the structure of prime rings with involution '*' such that _*[x, d(x)]_n ∈ Z(R) for all x ∈ R (for n = 1, 2), where d : R → R is a nonzero derivation of R. Among other related results, we also provide two examples to prove that the assumed restrictions on our main results are not superfluous.

• Korean Journal of Mathematics
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• v.30 no.1
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• pp.53-60
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• 2022

Let R be a finite commutative ring with non zero identity. The unit graph of R denoted by G(R) is the graph obtained by setting all the elements of R to be the vertices of a graph and two distinct vertices x and y are adjacent if and only if x + y ∈ U(R), where U(R) denotes the set of units of R. In this paper, we find the commutative rings R for which G(R) is a line graph. Also, we find the rings for which the complements of unit graphs are line graphs.

• Communications of the Korean Mathematical Society
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• v.38 no.4
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• pp.983-992
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• 2023

Let A be a ring and 𝓙 = {ideals I of A | J(I) = I}. The Krull dimension of A, written dim A, is the sup of the lengths of chains of prime ideals of A; whereas the dimension of the maximal spectrum, denoted by dim _𝓙A, is the sup of the lengths of chains of prime ideals from 𝓙. Then dim _𝓙A ≤ dim A. In this paper, we will study the dimension of the maximal spectrum of some constructions of rings and we will be interested in the transfer of the property J-Noetherian to ring extensions.

• Economic and Environmental Geology
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• v.40 no.4
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• pp.491-496
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• 2007

This study conducted a chemical experiment on the Leisegang phenomenon, which is known to be the principle of rhyolite formation, and analyzed the results. Even if the same chemical elements precipitated, the shape of Leisegang rings was different according to the condition of medium and depending on inner electrolyte and outer electrolyte. The experiment used agar, gelatin and mung-bean jelly as media. We prepared 0.01M inner electrolyte containing agar 1%, gelatin 2% and mung-bean jelly 5% and curdled the solution at room temperature for 12 hours and, as a result, we obtained viscosity optimal for experimenting on the diffusion of outer electrolyte, and Leisegang rings appeared clearly according to the characteristic of each chemical element. In $PbI_2$ with solubility product($K_{sp}$) of $7.9{\times}10^{-9}$ the intervals of Leisegang rings caused by the reaction of inner electrolyte 0.01M KI and outer electrolyte 25% $Pb(NO_3){_2}$ were narrow between 0.01cm and 0.12cmm but increased gradually, but in with of $8.3{\times}10^{-17}$ the intervals of Leisegang rings caused by the reaction of inner electrolyte 0.01M KI and outer electrolyte 25% $AgNO_3$ were between 0.7cm and 0.45cm and decreased gradually. This suggests that, in the chemical formation of Leisegang rings, the interval and size of the rings are correlated with the solubility product of the precipitates.

• The Korea Journal of Herbology
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• v.25 no.4
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• pp.69-75
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• 2010

Objectives : The root and rhizome of "Gangwhal" have been used as a traditional medicine for the treatment of cold, fever, headache, swelling, arthritis, rhinitis, and cardiovascular diseases in Korea and china. In china, Gangwhal is well known as a useful oriental medicinal plant that treats cardiovascular diseases such as stroke, headache and hypertension, but little research exists about the effect of O. koreanum on cardiovascular disease. Therefore we investigated the vasorelaxant effects of O. koreanum and compared the vasorelaxant effects of four species of Gangwhal. Methods : The vasorelaxant effects of the ethanol extracts of Ostericum koreanum (NK and BK), Notopterygium incisium (NI), and N. forbesii (NF) on phenyleprine ($1{\mu}M$) or KCl (60mM) pre-contracted rat thoracic aorta rings were compared. The vasorelaxant effects of the water extract and ethanol extract of NK on phenyleprine ($1{\mu}M$) or KCl (60mM) pre-contracted rat thoracic aorta rings were compared. And the vasorelaxant effects of chloroform, ethylacetate and water fraction of ethanol extract of NK on phenyleprine ($1{\mu}M$) or KCl (60mM) pre-contracted rat thoracic aorta rings were compared. Results : Ethanol extracts of NK, BK, NI and NF relaxed rat thoracic aorta rings with a concentration-dependent manner, and NK showed the greatest vasorelaxant effect. And ethanol extract of NK was much more effective than water extract of NK. Finally, chloroform, ethylacetate and water fraction of ethanol extract of NK also relaxed rat thoracic aorta rings, and chloroform fraction showed the greatest vasorelaxant effect.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.27 no.2
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• pp.79-93
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• 2015

Three-dimensional structures of large ocean rings in the Gulf Stream region are investigated using the HYbrid Coordinate Ocean Model (HYCOM). Numerically simulated flow structures around four selected cyclonic and anticyclonic rings are compared with two different horizontal resolutions: $1/12^{\circ}$ and $1/48^{\circ}$. The vertical distributions of Lagrangian Coherent Structures (LCSs) are analyzed using Finite Size Lyapunov Exponent (FSLE) and Okubo-Weiss parameters (OW). Curtain-shaped FSLE ridges are found in all four rings with extensions of surface ridges throughout the water columns, indicating that horizontal stirring is dominant over vertical motions. Near the high-resolution rings, many small-scale flow structures with size O(1~10) km are observed while these features are rarely found near the low-resolution rings. These small-scale structures affect the flow pattern around the rings as flow particles move more randomly in the high-resolution models. The dispersion rates are also affected by these small-scale structures as the relative horizontal dispersion coefficients are larger for the high-resolution models. The absolute vertical dispersion rates are, however, lower for the high-resolution models, because the particles tend to move along inclined eddy orbits when the resolution is low and this increases the magnitude of absolute vertical dispersion. Since relative vertical dispersion can reduce this effect from the orbital trajectories of particles, it gives a more reasonable magnitude range than absolute dispersion, and so is recommended in estimating vertical dispersion rates.

• East Asian mathematical journal
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• v.16 no.1
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• pp.33-48
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• 2000

In this paper, for any ring R with an identity, in order to study prime ideals of the endomorphism ring $End_R$(M) of left R-module $_RM$, meet-prime submodules, prime radical, sum-prime submodules and the prime socle of a module are defined. Some relations of the prime radical, the prime socle of a module and the prime radical of the endomorphism ring of a module are investigated. It is revealed that meet-prime(or sum-prime) modules and semi-meet-prime(or semi-sum-prime) modules have their prime, semi-prime endomorphism rings, respectively.

• Bulletin of the Korean Mathematical Society
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• v.38 no.4
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• pp.623-633
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• 2001

In this note we study the prime radicals of formal power series rings, and the shapes of them under the condition that the prime radical is nilpotent. Furthermore we observe the condition structurally, adding related examples to the situations that occur naturally in the process.

• Journal of the Chungcheong Mathematical Society
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• v.4 no.1
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• pp.99-102
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• 1991

Let R be a commutative ring with identity. A ring is said to be a regular multiplication ring if $A{\subseteq}B$, where A and B are ideals of R with B regular, implies that there exists an ideal C of R such that A = BC. We characterize such rings and study their properties.