• Journal of the Chungcheong Mathematical Society
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• v.22 no.3
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• pp.333-351
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• 2009

We introduce the concepts of strongly prime fuzzy ideals, powerful fuzzy ideals, strongly primary fuzzy ideals, and pseudo-strongly prime fuzzy ideals of an integral domain R and we provide characterizations of pseudo-valuation domains, almost pseudo-valuation domains, and pseudo-almost valuation domains in terms of these fuzzy ideals.

• 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.

• Honam Mathematical Journal
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• v.23 no.1
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• pp.21-28
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• 2001

In this short paper, we generalize some theorems about pseudo valuation domain to ring and give characterizations of psedo valuation ring.

• Korean Journal of Mathematics
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• v.18 no.2
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• pp.185-193
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• 2010

Let D be an integral domain, and let ${\bar{D}}$ be the integral closure of D. We show that if D is an almost pseudo-valuation domain (APVD), then D is a quasi-$Pr{\ddot{u}}fer$ domain if and only if D=P is a quasi-$Pr{\ddot{u}}fer$ domain for each prime ideal P of D, if and only if ${\bar{D}}$ is a valuation domain. We also show that D(X), the Nagata ring of D, is a locally APVD if and only if D is a locally APVD and ${\bar{D}}$ is a $Pr{\ddot{u}}fer$ domain.

• Communications of the Korean Mathematical Society
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• v.11 no.2
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• pp.281-284
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• 1996

In this paper we characterize strongly prime ideals and prove a theorem: an integral domain R is a PVD if and only if every maximal ideal M of R is strongly prime.

• 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.

• Bulletin of the Korean Mathematical Society
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• v.52 no.4
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• pp.1253-1268
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• 2015

It is well known that an integral domain D is a UFD if and only if every nonzero prime ideal of D contains a nonzero principal prime. This is the so-called Kaplansky's theorem. In this paper, we give this type of characterizations of a graded PvMD (resp., G-GCD domain, GCD domain, $B{\acute{e}}zout$ domain, valuation domain, Krull domain, ${\pi}$-domain).

• Proceedings of the Korean Operations and Management Science Society Conference
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• 2003.05a
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• pp.605-608
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• 2003

In order to satisfy the high need for technology valuation, various technology valuation methods have been developed. However the need to develop a new technology valuation method considering the technology characteristics, technology valuation objective, and technology valuation environments has been increasing. So far the technology valuation mehtods have been developed based on technology valuation experts' domain knowledge without applying systematic design methodology. In this paper the process that applies Axiomatic Design principles as a design methodology to the technology valuation methodology design is described. The design consists of technology valuation process design and technology valuation content design. The Axiomatic Design approach introduced in this paper can be used as a systematic technology valuation design tool considering various technology characteristics and technology valuation objectives and also as an evaluation tool of traditional technology methods.

• Bulletin of the Korean Mathematical Society
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• v.58 no.4
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• pp.897-908
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• 2021

In this paper, we introduce the notion of pseudo 2-prime ideals in commutative rings. Let R be a commutative ring with a nonzero identity. A proper ideal P of R is said to be a pseudo 2-prime ideal if whenever xy ∈ P for some x, y ∈ R, then x²ⁿ ∈ Pⁿ or y²ⁿ ∈ Pⁿ for some n ∈ ℕ. Various examples and properties of pseudo 2-prime ideals are given. We also characterize pseudo 2-prime ideals of PID's and von Neumann regular rings. Finally, we use pseudo 2-prime ideals to characterize almost valuation domains (AV-domains).

• Journal of the Chungcheong Mathematical Society
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• v.30 no.1
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• pp.53-59
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• 2017

In this article, we generalize the concepts of several classes of domains (which are related to a Dedekind domain) to a torsion-free module and it is shown that for a faithful multiplication module over an integral domain, we characterize Dedekind modules, cyclic submodule modules, and discrete valuation modules in terms of factorable modules and a sort of Euclidean algorithm.