• Korean Journal of Mathematics
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• 제8권1호
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• pp.87-90
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• 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.

• 충청수학회지
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• 제33권3호
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• pp.307-318
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• 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.

• 호남수학학술지
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• 제39권2호
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• pp.275-296
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• 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
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• 제45권2호
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• pp.249-254
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• 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
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• 제58권3호
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• pp.481-488
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• 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.

• 대한수학회보
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• 제61권3호
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• pp.797-811
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• 2024

In this paper, we define the torsion graph determined by equivalence classes of torsion elements and denote it by A_E(M). The vertex set of A_E(M) is the set of equivalence classes {[x] | x ∈ T(M)^*}, where two torsion elements x, y ∈ T(M)^* are equivalent if ann(x) = ann(y). Also, two distinct classes [x] and [y] are adjacent in A_E(M), provided that ann(x)ann(y)M = 0. We shall prove that for every torsion finitely generated module M over a Dedekind domain R, a vertex of A_E(M) has degree two if and only if it is an associated prime of M.

• 대한수학회보
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• 제51권2호
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• pp.329-338
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• 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.

• 대한지리학회지
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• 제52권1호
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• pp.73-103
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• 2017

이 논문은 현존하는 임진정계 경계표지 토퇴들의 분포와 특징에 대해 보고하고 있다. 그를 통해 목극등 지도에 표시된 '수출(水出)'의 위치를 확인하고자 하였다. 흑석구 동남안을 따라 설치된 토퇴들 중 마지막 토퇴의 위치는 대략 북위 $42^{\circ}04^{\prime}20.09^{{\prime}{\prime}}$, 동경 $128^{\circ}16^{\prime}08.42^{{\prime}{\prime}}$이다. '도화선 도로변 토퇴군'의 서쪽 시점은 대략 북위 $42^{\circ}02^{\prime}20.14^{{\prime}{\prime}}$, 동경 $128^{\circ}18^{\prime}53.40^{{\prime}{\prime}}$이며, 동쪽 종점의 좌표는 대략 북위 $42^{\circ}01^{\prime}32.97^{{\prime}{\prime}}$, 동경 $128^{\circ}21^{\prime}24.59^{{\prime}{\prime}}$이다. 서쪽 시점에서 약 2.1㎞ 지점까지는 대체적으로 "서-동"의 방향이며, 그 이동은 대체적으로 "서북-동남" 방향이다. 도화선 도로변 토퇴의 총 분포 길이는 실제거리 약 4.2㎞ 정도이다. 목극등 지도에 표시된 '수출'의 좌표는 대략 북위 $42^{\circ}01^{\prime}30.36^{{\prime}{\prime}}$, 동경 $128^{\circ}21^{\prime}3.62^{{\prime}{\prime}}$이다. 동쪽 마지막 토퇴의 동남 방향 지도상 평면 직선거리 약 222m 지점이다. 이러한 결과를 근거로 임진정계에 대한 재해석을 시도하였다.

• 대한수학회보
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• 제43권1호
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• pp.101-106
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• 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
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• 제31권1호
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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.