• 대한수학회보
• /
• 제46권5호
• /
• pp.867-871
• /
• 2009

A module M over a ring R is said to satisfy (P) if every generating set of M contains an independent generating set. The following results are proved; (1) Let $\tau$ = ($\mathbb{T}_\tau,\;\mathbb{F}_\tau$) be a hereditary torsion theory such that $\mathbb{T}_\tau$ $\neq$ Mod-R. Then every $\tau$-torsionfree R-module satisfies (P) if and only if S = R/$\tau$(R) is a division ring. (2) Let $\mathcal{K}$ be a hereditary pre-torsion class of modules. Then every module in $\mathcal{K}$ satisfies (P) if and only if either $\mathcal{K}$ = {0} or S = R/$Soc_\mathcal{K}$(R) is a division ring, where $Soc_\mathcal{K}$(R) = $\cap${I 4\leq$ $R_R$ : R/I$\in\mathcal{K}$}.

• 충청수학회지
• /
• 제30권1호
• /
• pp.77-102
• /
• 2017

As an analogy of $Poincar{\acute{e}}$ series in the space of modular forms, T. Ono associated a module $M_c/P_c$ for ${\gamma}=[c]{\in}H^1(G,R^{\times})$ where finite group G is acting on a ring R. $M_c/P_c$ is regarded as the 0-dimensional twisted Tate cohomology ${\hat{H}}^0(G,R^+)_{\gamma}$. In the case that G is the Galois group of a Galois extension K of a number field k and R is the ring of integers of K, the vanishing properties of $M_c/P_c$ are related to the ramification of K/k. We generalize this to arbitrary n-dimensional twisted cohomology of the ring of integers and obtain the extended version of theorems. Moreover, some explicit examples on quadratic and biquadratic number fields are given.

• 대한수학회지
• /
• 제48권3호
• /
• pp.627-639
• /
• 2011

Hopf corings are dened in this work as coring objects in the category of algebras over a commutative ring R. Using the Dieudonn$\'{e}$ equivalences from [7] and [19], one can associate coring structures built from the Hopf algebra $F_p[x_0,x_1,{\ldots}]$, p a prime, with Hopf ring structures with same underlying connected Hopf algebra. We have that $F_p[x_0,x_1,{\ldots}]$ coring structures classify thus Hopf ring structures for a given Hopf algebra. These methods are applied to dene new ring products in the Hopf algebras underlying known Hopf rings that come from connective Morava ${\kappa}$-theory.

• Bulletin of the Korean Chemical Society
• /
• 제10권6호
• /
• pp.500-503
• /
• 1989

Synthetic studies have been carried out for the addition or substitution of phosphorus nucleophiles to the cation $[(exo-6-R-{\eta}^ {5_-}2-MeO-C_6H_5)Mn(CO)_2NO]PF_6,$ 2. $PPh_3$ reacts with 2 to yield the CO displaced product and $MePPh_2$ attacks the dienyl ring of 2 to yield the phosphonium adduct or the metal to give the CO displaced depending upon the reaction temperatures. Nucleophilic addition of HPPh2 to the dienyl ring of 2 gives a neutral substituted product. $P(OMe)_3$ reacts with 2 to yield a mixture of ring adduct and CO displaced product at room temperature. $At - 20^{\circ}C,\;P(OMe)_3$ attacks the dienyl ring of 2 to give a posphonium adduct, which underwent Arbuzov reaction. This reaction affords a new route to the phosphonate complexes.

• 대한수학회보
• /
• 제28권2호
• /
• pp.175-180
• /
• 1991

In [3], [4] and [5], Hochster and Huneke introduced the notions of the tight closure of an ideal and of the weak F-regularity of a ring. This notion enabled us to give new proofs of many results in commutative algebra. A regular ring is known to be F-regular, and a Gorenstein local ring is proved to be F-regular provided that one ideal generated by a system of parameters (briefly s.o.p.) is tightly closed. In fact, a Gorenstein local ring is weakly F-regular if and only if there exists a system of parameters ideal which is tightly closed [3]. But we do not know whether this fact is true or not if a ring is not Gorenstein, in particular, a ring is a Cohen Macaulay (briefly C-M) local ring. In this paper, we will prove this in the case of an 1-dimensional C-M local ring. For this, we study the F-rationality and the normality of the ring. And we will also prove that a C-M local ring is to be Gorenstein under some additional condition about the tight closure.

• Journal of the Korean Wood Science and Technology
• /
• 제45권5호
• /
• pp.661-670
• /
• 2017

지리산 아고산대 주요 침엽수(주목, 잣나무, 구상나무)와 신갈나무를 이용하여 50년간의 산소동위원소연대기(1966~2015)를 작성하였다. 산소동위원소연대기 작성은 크로스데이팅(cross-dating) 결과가 우수한 4본을 각 수종에서 선발하여 실시하였다. 동일 수종 내 임목 간 산소동위원소연대기의 상관분석 결과 모두 유의성(p < 0.001) 높은 상관이 있는 것으로 확인되었으며, EPS도 0.85 이상이었다. 동일 수종 내 임목 간 상관분석뿐만 아니라 수종간 상관분석에서도 유의성(p < 0.001) 높은 상관관계가 확인되었다. 기후요소(강수량, 기온)와 산소동위원소와의 관계를 조사하기 위한 반응함수 분석에서 주목은 당년 5월 강수량과 유의성 있는 부의 상관을 보였으며, 구상나무는 4월 강수량과 유의성 있는 부의 상관을 보였다. 향후 주목과 구상나무에 대한 장기간의 산소동위원소연대기가 작성된다면 과거 측정하지 못한 장기간의 4월과 5월 강수량 복원이 가능할 것이다.

• 대한수학회보
• /
• 제54권4호
• /
• pp.1281-1291
• /
• 2017

Let R be a strongly 2-primal ring and I a proper ideal of R. Then there are only finitely many prime ideals minimal over I if and only if for every prime ideal P minimal over I, the ideal $P/{\sqrt{I}}$ of $R/{\sqrt{I}}$ is finitely generated if and only if the ring $R/{\sqrt{I}}$ satisfies the ACC on right annihilators. This result extends "D. D. Anderson, A note on minimal prime ideals, Proc. Amer. Math. Soc. 122 (1994), no. 1, 13-14." to large classes of noncommutative rings. It is also shown that, a 2-primal ring R only has finitely many minimal prime ideals if each minimal prime ideal of R is finitely generated. Examples are provided to illustrate our results.

• Journal of the Optical Society of Korea
• /
• 제16권2호
• /
• pp.157-161
• /
• 2012

This work reports the stability of the resonant characteristics in multimode interferometer coupled square ring semiconductor cavities. Based on the analysis of single square ring cavities, the single mode operations in the multimode interferometer coupled ring cavities are analyzed and the devices are demonstrated on the semiconductor multiple quantum well epitaxial structure. By varying the lasing conditions such as substrate temperature and input pump power, single resonant mode operations are also observed.

• 대한전자공학회:학술대회논문집
• /
• 대한전자공학회 2007년도 하계종합학술대회 논문집
• /
• pp.223-224
• /
• 2007

To develop nuclear measurement system with characteristics including both re-configuration and multi-functions, we proposed a field programmable gate array (FPGA) technique to implement TDC which is more suitable for high energy Physics system. In TDC scheme, the timing resolution is more important than the count rates of channel. In order to manage pico-second resolution TDC, we used the delay components of FPGA, utilized the place and route (P&R) delay difference, and then got two ring oscillators. By setting P&R area constraints, we generated two precise ring oscillators with slightly different frequencies. Finally, we evaluated that the period difference of these two ring oscillators was about 60 pico-seconds, timing resolution of TDC.

• 대한수학회지
• /
• 제61권5호
• /
• pp.953-973
• /
• 2024

Let R = ⊕_α∈Γ R_α be a commutative ring graded by an arbitrary torsionless monoid Γ. A homogeneous prime ideal P of R is said to be strongly homogeneous prime if aP and bR are comparable for any homogeneous elements a, b of R. We will say that R is a graded pseudo-valuation ring (gr-PVR for short) if every homogeneous prime ideal of R is strongly homogeneous prime. In this paper, we introduce and study the graded version of the pseudo-valuation rings which is a generalization of the gr-pseudo-valuation domains in the context of arbitrary Γ-graded rings (with zero-divisors). We then study the possible transfer of this property to the graded trivial ring extension and the graded amalgamation. Our goal is to provide examples of new classes of Γ-graded rings that satisfy the above mentioned property.