• Korean Journal of Mathematics
• /
• v.8 no.1
• /
• pp.87-90
• /
• 2000

Let R be an integral domain with identity. We show that each associated prime ideal of a principal ideal in R[X] has height one if and only if each associated prime ideal of a principal ideal in R has height one and R is an S-domain.

• Journal of the Chungcheong Mathematical Society
• /
• v.33 no.3
• /
• pp.307-318
• /
• 2020

In this paper, we extend the notion of a generalized derivation F associated with derivation d to two generalized derivations F and G associated with the same derivation d, as a new idea, to obtain the commutativity of prime rings under certain conditions.

• Honam Mathematical Journal
• /
• v.39 no.2
• /
• pp.275-296
• /
• 2017

All rings considered here are commutative rings with identity and all modules considered here are unital left modules. A submodule N of an R-module M is said to be extended to M if $N=aM$ for some ideal a of R and it is said to be fully invariant if ${\varphi}(L){\subseteq}L$ for every ${\varphi}{\in}End(M)$. An R-module M is called a [resp., fully invariant] multiplication module if every [resp., fully invariant] submodule is extended to M. The class of fully invariant multiplication modules is bigger than the class of multiplication modules. We deal with prime submodules and associated prime submodules of fully invariant multiplication modules. In particular, when M is a nonzero faithful multiplication module over a Noetherian ring, we characterize the zero-divisors of M in terms of the associated prime submodules, and we show that the set Aps(M) of associated prime submodules of M determines the set $Zdv_M(M)$ of zero-dvisors of M and the support Supp(M) of M.

• Kyungpook Mathematical Journal
• /
• v.45 no.2
• /
• pp.249-254
• /
• 2005

Let N be a prime left near-ring with multiplicative center Z and f be a generalized $({\sigma},{\tau})-derivation$ associated with d. We prove commutativity theorems in prime near- rings with generalized $({\sigma},{\tau})-derivation$.

• Kyungpook Mathematical Journal
• /
• v.58 no.3
• /
• pp.481-488
• /
• 2018

Let I be a ${\ast}$-ideal on a 2-torsion free ${\ast}$-prime ring and $F:R{\rightarrow}R$ a generalized derivation with an associated derivation $d:R{\rightarrow}R$. The aim of this paper is to explore the condition under which generalized derivation F becomes a left centralizer i.e., associated derivation d becomes a trivial map (i.e., zero map) on R.

• Bulletin of the Korean Mathematical Society
• /
• v.51 no.2
• /
• pp.329-338
• /
• 2014

In this paper, we study the method of upper and lower solutions and develop the generalized quasilinearization technique for the existence and approximation of solutions to some three-point nonlocal boundary value problems associated with higher order fractional differential equations of the type $$^c{\mathcal{D}}^q_{0+}u(t)+f(t,u(t))=0,\;t{\in}(0,1)$$ $$u^{\prime}(0)={\gamma}u^{\prime}({\eta}),\;u^{\prime\prime}(0)=0,\;u^{\prime\prime\prime}(0)=0,{\ldots},u^{(n-1)}(0)=0,\;u(1)={\delta}u({\eta})$$, where, n-1 < q < n, $n({\geq}3){\in}\mathbb{N}$, 0 < ${\eta},{\gamma},{\delta}$ < 1 and $^c\mathcal{D}^q_{0+}$ is the Caputo fractional derivative of order q. The nonlinear function f is assumed to be continuous.

• Journal of the Korean Geographical Society
• /
• v.52 no.1
• /
• pp.73-103
• /
• 2017

This paper reports the distribution of soil piles set up during the Yimjin(1712) Boundary Making and Demarcation(YBMD). Through the survey on the distribution of soil piles the location of 'Suchul'(水出: seepage zone) could be identified. The endpoint soil pile set up on the east-south bank of Heishigou(黑石溝) stream locates on $42^{\circ}04^{\prime}20.09^{{\prime}{\prime}}N$, $128^{\circ}16^{\prime}08.42^{{\prime}{\prime}}E$. The west beginning point of soil piles distributed in the south side of Tuhexian road locates on $42^{\circ}02^{\prime}20.14^{{\prime}{\prime}}N$, $128^{\circ}18^{\prime}53.40^{{\prime}{\prime}}E$. And the east endpoint of them locates $42^{\circ}01^{\prime}32.97^{{\prime}{\prime}}N$, $128^{\circ}21^{\prime}24.59^{{\prime}{\prime}}E$. From the west beginning point to the soil pile located in 2.1km distance from the beginning point, the distribution direction is west-east. The direction of soil piles after them is northwest-southeast. The total real length of soil piles distributed in the south side of Tuhexian(圖和線) road is about 4.2km more or less. The location of 'Suchul' written on the Mukedeng's map locates on $42^{\circ}01^{\prime}30.36^{{\prime}{\prime}}N$, $128^{\circ}21^{\prime}3.62^{{\prime}{\prime}}E$, The point locates in southeastward 222m distance from the soil piles endpoint of the south side of Tuhexian road. In reference of these reports this paper develops some reinterpretation on the YBMD.

• Bulletin of the Korean Mathematical Society
• /
• v.43 no.1
• /
• pp.101-106
• /
• 2006

Let R be a prime ring and I a nonzero ideal of R. Let $\alpha,\;\nu,\;\tau\;R{\rightarrow}R$ be the endomorphisms and $\beta,\;\mu\;R{\rightarrow}R$ the automorphisms. If R admits a generalized $(\alpha,\;\beta)-derivation$ g associated with a nonzero $(\alpha,\;\beta)-derivation\;\delta$ such that $g([\mu(x),y])\;=\;[\nu/(x),y]\alpha,\;\tau$ for all x, y ${\in}I$, then R is commutative.

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

• Economic and Environmental Geology
• /
• v.3 no.2
• /
• pp.55-73
• /
• 1970

The district investigated covers the central and southern portions of the Uiryong Quadrangle amounting to $40km^2$ in area and is bounded approximately by geographical coordinates of $128^{\circ}$ 28' $40^{{\prime}{\prime}}{\sim}128^{\circ}$ 24' 25"E in longitude and $35^{\circ}10{\prime}{\sim}35^{\circ}14^{\prime}06^{{\prime}{\prime}}N$ in latitude. The purpose of this investigation was to provide basic information in drawing up a comprehensive development plan of the copper ore deposits known to exist in the HamanKumbuk district with special emphasis given to the ascertainment of geological and paragenetic characteristics. The area consists chiefly of shale, sandy shale and chert, all belong to Kyongsang System of Cretaceous age. Intruded into these rocks are andesite, granodiorite, basic dikes, and acidic dikes. The mineralization which took place in the area, consists of mostly fissure-filling vein deposits, numbering several tens, with varying magnitudes. The fissures and shear zones created in rocks, such as chert and granodiorite, hosted the deposition of mineralizing vapors and/or hydrothermal solutions along their openings. The strike lengths of these veins vary from 50 to 600 meters in extension and 0.1 to 3 meters in width. Although the degree of fluctuation in width is great, it averages 0.3m. The stuctural patterns, which apparently affected the deposition of veins, are fissure patterns, trend NS to $N30^{\circ}W$, and steep-pitching tension fractures as well as normal fault pattern. Ore minerals associated with vein matters are primarily chalcopyrite and small amounts of scheelite, cobaltiferous arsenopyrite, and gold and silver intimately associated with sulphide minerals. Associated with these ore mineral are pyrite, pyrrhotite, magnetite, specularite and arsenopyrite. Gangue minerals noted are quartz, calcite, chlorite, tourmaline and hornblende. In terms of the compositions of associated minerals, the vein deposits in the district could be grouped under the following four categories: 1. Pyrrhoitite, Arsenopyrite, Gold and Silver Bearing Copper Vein (Type I) 2. Calcite-Scheelite-Copper Vein (Type II) 3. Magnetite-Pyrite-Copper Vein (Type III) 4. Tourmaline Copper Vein (Type IV) Of the four types, the first and the fourth are presently yielding relatively higher grades: of copper ores and concentrates. The estimated ore reserves total some 222,000 metric tons with the following breakdown in terms of metal contents: Name of Mines Au(g/t) Ag(g/t) Cu(%) Reserves(M/T) Kunbuk 15.92 78.69 6,074 60.498 Cheil Kunbuk - - 1.040 60,847 Haman - - 2.688 101,204 222,549 As rehabilitation of old workings and/or exploration of veins at depth proceed, additional estimation of ore reserves may become apparent and necessary. With regard to the problem of beneficiation and upgrading of low-grade ores in the district, it would be advisable to make decisions on location, treating capacity and mill flowsheet after sufficient amount of exploration is completed as suggested in the report.