• Journal of applied mathematics & informatics
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• v.28 no.3_4
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• pp.1017-1023
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• 2010

We prove that a maximal ideal M of D[x] has two generators and is of the form where p is an irreducible element in a PID D having infinitely many nonassociate irreducible elements and q(x) is an irreducible non-constant polynomial in D[x]. Moreover, we find how minimal generators of maximal ideals of a polynomial ring D[x] over a DVR D consist of and how many generators those maximal ideals have.

• Kyungpook Mathematical Journal
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• v.55 no.4
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• pp.817-826
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• 2015

Let R be a commutative ring with total quotient ring K. Each monomorphic R-module endomorphism of a cyclic R-module is an isomorphism if and only if R has Krull dimension 0. Each monomorphic R-module endomorphism of R is an isomorphism if and only if R = K. We say that R has property (${\star}$) if for each nonzero element $a{\in}R$, each monomorphic R-module endomorphism of R/Ra is an isomorphism. If R has property (${\star}$), then each nonzero principal prime ideal of R is a maximal ideal, but the converse is false, even for integral domains of Krull dimension 2. An integral domain R has property (${\star}$) if and only if R has no R-sequence of length 2; the "if" assertion fails in general for non-domain rings R. Each treed domain has property (${\star}$), but the converse is false.

• Kyungpook Mathematical Journal
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• v.51 no.1
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• pp.1-10
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• 2011

Let (R, T) be a normal pair of commutative rings (i.e., R ${\subseteq}$ T is a unita extension of commutative rings, not necessarily integral domains, such that S is integrally closed in T for each ring S such that R ${\subseteq}$ S ${\subseteq}$ T) such that the total quotient ring of R is a von Neumann regular ring. Let P be one of the following ring-theoretic properties: going-down ring, extensionally going-down (EGD) ring, locally divided ring. Then R has P if and only if T has P. An example shows that the "if" part of the assertion fails if P is taken to be the "divided domain" property.

• Communications of the Korean Mathematical Society
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• v.38 no.1
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• pp.11-19
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• 2023

Let 𝓗₀ be the set of rings R such that Nil(R) = Z(R) is a divided prime ideal of R. The concept of maximal non φ-chained subrings is a generalization of maximal non valuation subrings from domains to rings in 𝓗₀. This generalization was introduced in [20] where the authors proved that if R ∈ 𝓗₀ is an integrally closed ring with finite Krull dimension, then R is a maximal non φ-chained subring of T(R) if and only if R is not local and |[R, T(R)]| = dim(R) + 3. This motivates us to investigate the other natural numbers n for which R is a maximal non φ-chained subring of some overring S. The existence of such an overring S of R is shown for 3 ≤ n ≤ 6, and no such overring exists for n = 7.

• Journal of Software Assessment and Valuation
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• v.16 no.2
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• pp.143-151
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• 2020

The digital content's security and authentication are important in the field of digital content application. There are some methods to perform the authentication. The digital watermarking is one of authentication methods. Paper presents a digital watermark authentication method that works in the application of digital image. The proposed watermark has the triple status information and performs the embedding and the detection without original Content. When authenticating the owner information of digital content, an autocorrelation function is used. In addition, a spread spectrum method is used to be adaptive to the signal of the original content in the frequency domain(DWT Domain). Therefore, the possibility of errors occurring in the detection of hidden information was reduced. it also has a advantage what Watermarking in DWT has faster embedding and detection time than other transformation domains(DFT, DCT, etc.). if it has a an image of size N=mXm, the computational amount can be reduced from O(N·logN) to O(N). The particular advantage is that it can hide more information(bits) per bit.

• The KIPS Transactions:PartB
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• v.8B no.6
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• pp.601-608
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• 2001

The automated assignment of multiple tasks to executing agents is a key problem in the area of multi-agent systems. In many domains, significant savings can be achieved by reallocating tasks among agents with different costs for handling tasks. The automation of task reallocation among self-interested agents requires that the individual agents use a common negotiation protocol that prescribes how they have to interact in order to come to an agreement on "who does what". In this paper, we introduce the multi-agent Traveling Salesman Problem(TSP) as an example of task reallocation problem, and suggest the Vickery auction as an interagent negotiation protocol for solving this problem. In general, auction-based protocols show several advantageous features: they are easily implementable, they enforce an efficient assignment process, and they guarantce an agreement even in scenarios in which the agents possess only very little domain-specific Knowledge. Furthermore Vickrey auctions have the additional advantage that each interested agent bids only once and that the dominant strategy is to bid one′s true valuation. In order to apply this market-based protocol into task reallocation among self-interested agents, we define the profit of each agent, the goal of negotiation, tasks to be traded out through auctions, the bidding strategy, and the sequence of auctions. Through several experiments with sample multi-agent TSPs, we show that the task allocation can improve monotonically at each step and then finally an optimal task allocation can be found with this protocol.

• Journal of Korean Society of Rural Planning
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• v.20 no.4
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• pp.101-112
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• 2014

The public value of agriculture and rural areas is closely associated with the concept of multifunctionality of agriculture and rural areas, which in turn signifies economic values other than the production function of agriculture and rural areas. Based on the survey results, virtual scenarios were set up and the contingent valuation method (CVM) was used to estimate the amount consumers are willing to pay (WTP) for the public functions of agriculture and rural areas. This study selected five domains of the public value (environment conservation, maintenance of landscape and cultural tradition, enhancement of national prestige, local community maintenance and socio-economic functions, and food security) and 21 value items as components of the public value. An economic assessment of the public value of agriculture and rural areas was conducted using a binomial logistic regression model. The estimation results showed that the public value consumers are willing to pay ranges from a minimum of 6,346.8 billion won to a maximum of 9,327.2 billion won.

• Journal of the Korean Mathematical Society
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• v.59 no.3
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• pp.571-594
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• 2022

Let D be an integral domain with quotient field K, Pic(D) be the ideal class group of D, and X be an indeterminate. A polynomial overring of D means a subring of K[X] containing D[X]. In this paper, we study almost Dedekind domains which are polynomial overrings of a principal ideal domain D, defined by the intersection of K[X] and rank-one discrete valuation rings with quotient field K(X), and their ideal class groups. Next, let ℤ be the ring of integers, ℚ be the field of rational numbers, and 𝔊f be the set of finitely generated abelian groups (up to isomorphism). As an application, among other things, we show that there exists an overring R of ℤ[X] such that (i) R is a Bezout domain, (ii) R∩ℚ[X] is an almost Dedekind domain, (iii) Pic(R∩ℚ[X]) = $\oplus_{G{\in}G_{f}}$ G, (iv) for each G ∈ 𝔊f, there is a multiplicative subset S of ℤ such that RS ∩ ℚ[X] is a Dedekind domain with Pic(RS ∩ ℚ[X]) = G, and (v) every invertible integral ideal I of R ∩ ℚ[X] can be written uniquely as I = XnQe11···Qekk for some integer n ≥ 0, maximal ideals Qi of R∩ℚ[X], and integers ei ≠ 0. We also completely characterize the almost Dedekind polynomial overrings of ℤ containing Int(ℤ).