• Honam Mathematical Journal
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• v.39 no.2
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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.

• Journal of the Korean Mathematical Society
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• v.54 no.6
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• pp.1733-1757
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• 2017

Let $R={\oplus}_{{\alpha}{\in}{\Gamma}}R_{\alpha}$ be an integral domain graded by an arbitrary torsionless grading monoid ${\Gamma}$, ${\bar{R}}$ be the integral closure of R, H be the set of nonzero homogeneous elements of R, C(f) be the fractional ideal of R generated by the homogeneous components of $f{\in}R_H$, and $N(H)=\{f{\in}R{\mid}C(f)_v=R\}$. Let $R_H$ be a UFD. We say that a nonzero prime ideal Q of R is an upper to zero in R if $Q=fR_H{\cap}R$ for some $f{\in}R$ and that R is a graded UMT-domain if each upper to zero in R is a maximal t-ideal. In this paper, we study several ring-theoretic properties of graded UMT-domains. Among other things, we prove that if R has a unit of nonzero degree, then R is a graded UMT-domain if and only if every prime ideal of $R_{N(H)}$ is extended from a homogeneous ideal of R, if and only if ${\bar{R}}_{H{\backslash}Q}$ is a graded-$Pr{\ddot{u}}fer$ domain for all homogeneous maximal t-ideals Q of R, if and only if ${\bar{R}}_{N(H)}$ is a $Pr{\ddot{u}}fer$ domain, if and only if R is a UMT-domain.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.32 no.5A
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• pp.307-315
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• 2012

Recently, ultra high performance fiber reinforced concrete (UHPFRC) having over 180 MPa compressive strength and 10 MPa tensile strength has been developed in Korea. However, UHPFRC represents different material properties with normal concrete (NC) and conventional high performance concrete (HPC) such as a high early age autogenous shrinkage and a rapid dry on the surface, because it has a low water-binder ratio and high fineness admixtures without coarse aggregate. In this study, therefore, to propose suitable experimental methods and regulations, and to evaluate mechanical properties at a very early age for UHPFRC, setting, shrinkage and tensile tests were performed. From the setting test results, paraffin oil was an appropriate material to prevent drying effect on the surface, because if paraffin oil is applied on the surface, it can efficiently prevent the drying effect and does not disturb or catalyze the hydration of cement. From the ring-test results, it was defined that the shrinkage stress is generated at the time when the graph tendency of temperature and strain of inner steel ring is changed. By comparing with setting test result, the shrinkage stress was firstly occurred as the penetration resistance of 1.5 MPa was obtained, and it was about 0.6 and 2.1 hour faster than those of initial and final sets. So, the starting time of autogenous shrinkage measurement (time-zero) of UHPFRC was determined when the penetration resistance of 1.5 MPa was obtained. Finally, the tensile strength and elastic modulus of UHPFRC were measured from near initial setting time by using a very early age tensile test apparatus, and the prediction models for tensile strength and elastic modulus were proposed.

• Journal of Communications and Networks
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• v.14 no.6
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• pp.653-661
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• 2012

High-availability seamless redundancy (HSR) is a redundancy protocol for Ethernet networks that provides two frame copies for each frame sent. Each copy will pass through separate physical paths, pursuing zero fault recovery time. This means that even in the case of a node or a link failure, there is no stoppage of network operations whatsoever. HSR is a potential candidate for the communications of a smart grid, but its main drawback is the unnecessary traffic created due to the duplicated copies of each sent frame, which are generated and circulated inside the network. This downside will degrade network performance and might cause network congestion or even stoppage. In this paper, we present two approaches to solve the above-mentioned problem. The first approach is called quick removing (QR), and is suited to ring or connected ring topologies. The idea is to remove the duplicated frame copies from the network when all the nodes have received one copy of the sent frame and begin to receive the second copy. Therefore, the forwarding of those frame copies until they reach the source node, as occurs in standard HSR, is not needed in QR. Our example shows a traffic reduction of 37.5%compared to the standard HSR protocol. The second approach is called the virtual ring (VRing), which divides any closed-loop HSR network into several VRings. Each VRing will circulate the traffic of a corresponding group of nodes within it. Therefore, the traffic in that group will not affect any of the other network links or nodes, which results in an enhancement of traffic performance. For our sample network, the VRing approach shows a network traffic reduction in the range of 67.7 to 48.4%in a healthy network case and 89.7 to 44.8%in a faulty network case, compared to standard HSR.

• Korean Journal of Optics and Photonics
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• v.14 no.6
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• pp.649-656
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• 2003

In this paper we confirm the relation between the phase and phase error of the beat signal at the lock-in region of the dither type ring laser gyroscope by numerical calculation. We also study the requirement of the dither noise of an amplitude modulation type for statistical zero averaging of the beat signal phase error, without accumulation. As a result, we find that the dither noise requires the increase and decrease gradients of the dither amplitude, and those gradients should be combined with similar white noise. The slope of the gradient and maximum/minimum amplitude must be changed randomly. We confirm the error accumulation characteristic related to the dither noise by comparison of the two outputs during temperature change, by operating the two kinds dither noise, one is satisfied with the requirement and the other is not.

• Korean Journal of Mathematics
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• v.19 no.2
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• pp.163-169
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• 2011

Let D be an integral domain, S be a multiplicative subset of D such that DS is a PID, and D[X] be the polynomial ring over D. We show that S is an almost splitting set in D if and only if every nonzero prime ideal of D disjoint from S contains a primary element. We use this result to give a simple proof of the known result that D is a UMT-domain and Cl(D[X]) is torsion if and only if each upper to zero in D[X] contains a primary element.

• 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.50 no.2
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• pp.649-657
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• 2013

Let R be a commutative Noetherian ring, I an ideal of R and T be a non-zero I-cofinite R-module with dim(T) ${\leq}$ 1. In this paper, for any finitely generated R-module N with support in V(I), we show that the R-modules $Ext^i_R$(T,N) are finitely generated for all integers $i{\geq}0$. This immediately implies that if I has dimension one (i.e., dim R/I = 1), then $Ext^i_R$($H^j_I$(M), N) is finitely generated for all integers $i$, $j{\geq}0$, and all finitely generated R-modules M and N, with Supp(N) ${\subseteq}$ V(I).

• Journal of the Korean Mathematical Society
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• v.54 no.4
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• pp.1099-1108
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• 2017

Let R be a commutative ring with non-zero identity and M be a unitary R-module. Let S(M) be the set of all submodules of M and ${\phi}:S(M){\rightarrow}S(M){\cup}\{{\emptyset}\}$ be a function. We say that a proper submodule P of M is a ${\phi}$-semiprime submodule if $r{\in}R$ and $x{\in}M$ with $r^2x{\in}P{\setminus}{\phi}(P)$ implies that $rx{\in}P$. In this paper, we investigate some properties of this class of sub-modules. Also, some characterizations of ${\phi}$-semiprime submodules are given.

• 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.