• Bulletin of the Korean Mathematical Society
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• v.50 no.3
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• pp.719-725
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• 2013

A domain is called an LPI domain if every locally principal ideal is invertible. It is proved in this note that if D is a LPI domain, then D[X] is also an LPI domain. This fact gives a positive answer to an open question put forward by D. D. Anderson and M. Zafrullah.

• Journal of the Korean Ceramic Society
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• v.25 no.6
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• pp.699-703
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• 1988

Domain structures of LiNbO3 crystals grown by Czochralski method were examined according to the growth axis and the rotational speed of crystals. Ring shape and split domain structures were revealed in Z-axis and Y-axis grown crystals respectively. It was found that the domain structures of grown crystals were closely related to the solid-liquid interface shape during growth.

• Korean Journal of Mathematics
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• v.25 no.2
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• pp.215-227
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• 2017

Let D be an integral domain with quotient field K, X be an indeterminate over D, K[X] be the polynomial ring over K, and $R=\{f{\in}K[X]{\mid}f(0){\in}D\}$; so R is a subring of K[X] containing D[X]. For $f=a_0+a_1X+{\cdots}+a_nX^n{\in}R$, let C(f) be the ideal of R generated by $a_0$, $a_1X$, ${\ldots}$, $a_nX^n$ and $N(H)=\{g{\in}R{\mid}C(g)_{\upsilon}=R\}$. In this paper, we study two rings $R_{N(H)}$ and $Kr(R,{\upsilon})=\{{\frac{f}{g}}{\mid}f,g{\in}R,\;g{\neq}0,{\text{ and }}C(f){\subseteq}C(g)_{\upsilon}\}$. We then use these two rings to give some examples which show that the results of [4] are the best generalizations of Nagata rings and Kronecker function rings to graded integral domains.

• Bulletin of the Korean Mathematical Society
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• v.52 no.4
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• pp.1327-1338
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• 2015

In this paper, we introduce and study the w-weak global dimension w-w.gl.dim(R) of a commutative ring R. As an application, it is shown that an integral domain R is a $Pr\ddot{u}fer$ v-multiplication domain if and only if w-w.gl.dim(R) ${\leq}1$. We also show that there is a large class of domains in which Hilbert's syzygy Theorem for the w-weak global dimension does not hold. Namely, we prove that if R is an integral domain (but not a field) for which the polynomial ring R[x] is w-coherent, then w-w.gl.dim(R[x]) = w-w.gl.dim(R).

• Kyungpook Mathematical Journal
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• v.57 no.2
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• pp.187-191
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• 2017

Let R be a domain with quotient field K and prime subring A. Then R is integral over each of its subrings having quotient field K if and only if (A, R) is a survival pair. This shows the redundancy of a condition involving going-down pairs in a earlier characterization of such rings. In characteristic 0, the domains being characterized are the rings R that are isomorphic to subrings of the ring of all algebraic integers. In positive (prime) characteristic, the domains R being characterized are of two kinds: either R = K is an algebraic field extension of A or precisely one valuation domain of K does not contain R.

• Korean Journal of Mathematics
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• v.17 no.3
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• pp.245-248
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• 2009

We consider pm-ring with the property such that every prime ideal is contained in only one maximal ideal. Orsatti[4] characterized pm-rings by means of the retraction. Contessa[1] found algebraic condition, by using that direct product of pm-rings is a pm-ring. We show that C(X, H) and C(X, C) are pm-rings and we extend a quasi pm-domain.

• Journal of the Korean Mathematical Society
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• v.45 no.5
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• pp.1405-1416
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• 2008

Let D be an integral domain, X an indeterminate over D, $N_v = \{f{\in}D[X]|(A_f)_v=D\}.$. Among other things, we introduce the concept of t-locally PVDs and prove that $D[X]N_v$ is a locally PVD if and only if D is a t-locally PVD and a UMT-domain, if and only if D[X] is a t-locally PVD, if and only if each overring of $D[X]N_v$ is a locally PVD.

• Communications of the Korean Mathematical Society
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• v.39 no.1
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• pp.71-77
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• 2024

Let A be a commutative integral domain with identity element and S a multiplicatively closed subset of A. In this paper, we introduce the concept of S-valuation domains as follows. The ring A is said to be an S-valuation domain if for every two ideals I and J of A, there exists s ∈ S such that either sI ⊆ J or sJ ⊆ I. We investigate some basic properties of S-valuation domains. Many examples and counterexamples are provided.

• Parasites, Hosts and Diseases
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• v.53 no.1
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• pp.65-75
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• 2015

Clonorchis sinensis habitating in the bile duct of mammals causes clonorchiasis endemic in East Asian countries. Parkin is a RING-between-RING protein and has E3-ubiquitin ligase activity catalyzing ubiquitination and degradation of substrate proteins. A cDNA clone of C. sinensis was predicted to encode a polypeptide homologous to parkin (CsParkin) including 5 domains (Ubl, RING0, RING1, IBR, and RING2). The cysteine and histidine residues binding to $Zn^{2+}$ were all conserved and participated in formation of tertiary structural RINGs. Conserved residues were also an E2-binding site in RING1 domain and a catalytic cysteine residue in the RING2 domain. Native CsParkin was determined to have an estimated molecular weight of 45.7 kDa from C. sinensis adults by immunoblotting. CsParkin revealed E3-ubiquitin ligase activity and higher expression in metacercariae than in adults. CsParkin was localized in the locomotive and male reproductive organs of C. sinensis adults, and extensively in metacercariae. Parkin has been found to participate in regulating mitochondrial function and energy metabolism in mammalian cells. From these results, it is suggested that CsParkin play roles in energy metabolism of the locomotive organs, and possibly in protein metabolism of the reproductive organs of C. sinensis.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.37 no.4
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• pp.537-545
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• 2013

The elastic recovery of a metal seal is a factor that can be used to assess its sealing performance. In this study, a compliant mechanism topology optimization has been performed to find a structure of a metal O-ring seal that can maintain excellent sealing performance with a maximized elastic recovery over extended operation. An evolutionary structural optimization (ESO) was used as a topology optimization algorithm with two different types of objective functions considering both flexibility and stiffness. In particular, a circular design domain was adopted to consider the outer shape of the metal O-ring seal. The elastic recovery of the optimal topology was calculated and compared to that of a commercial product.