• 호남수학학술지
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• 제31권4호
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• pp.639-644
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• 2009

In this paper, we begin with to introduce the concepts of IFP and strong IFP in near-rings and then give some characterizations of IFP in near-rings. Next we derive reversible IFP, and then equivalences of the concepts of strong IFP and strong reversibility. Finally, we obtain some conditions to become strong IFP in right permutable near-rings and strongly reversible near-rings.

• 대한수학회보
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• 제44권1호
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• pp.87-94
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• 2007

We in this note introduce the concept of g-IFP rings which is a generalization of IFP rings. We show that from any IFP ring there can be constructed a right g-IFP ring but not IFP. We also study the basic properties of right g-IFP rings, constructing suitable examples to the situations raised naturally in the process.

• Korean Journal of Mathematics
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• 제23권1호
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• pp.37-46
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• 2015

We in this note introduce the concept of semi-IFP rings which is a generalization of IFP rings. We study the basic structure of semi-IFP rings, and construct suitable examples to the situations raised naturally in the process. We also show that the semi-IFP does not go up to polynomial rings.

• 대한수학회지
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• 제46권5호
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• pp.1027-1040
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• 2009

A ring R is called IFP, due to Bell, if ab = 0 implies aRb = 0 for a, b $\in$ R. Huh et al. showed that the IFP condition is not preserved by polynomial ring extensions. In this note we concentrate on a generalized condition of the IFPness that can be lifted up to polynomial rings, introducing the concept of quasi-IFP rings. The structure of quasi-IFP rings will be studied, characterizing quasi-IFP rings via minimal strongly prime ideals. The connections between quasi-IFP rings and related concepts are also observed in various situations, constructing necessary examples in the process. The structure of minimal noncommutative (quasi-)IFP rings is also observed.

• 대한수학회지
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• 제45권3호
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• pp.727-740
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• 2008

A ring R is called IFP, due to Bell, if ab=0 implies aRb=0 for $a,b{\in}R$. Huh et al. showed that the IFP condition need not be preserved by polynomial ring extensions. But it is shown that ${\sum}^n_{i=0}$ $E_{ai}E$ is a nonzero nilpotent ideal of E whenever R is an IFP ring and $0{\neq}f{\in}F$ is nilpotent, where E is a polynomial ring over R, F is a polynomial ring over E, and $a_i^{'s}$ are the coefficients of f. we shall use the term near IFP to denote such a ring as having place near at the IFPness. In the present note the structures of IFP rings and near-IFP rings are observed, extending the classes of them. IFP rings are NI (i.e., nilpotent elements form an ideal). It is shown that the near-IFPness and the NIness are distinct each other, and the relations among them and related conditions are examined.

• 대한수학회지
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• 제52권6호
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• pp.1161-1178
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• 2015

In this paper, we investigate the insertion-of-factors-property (simply, IFP) on skew polynomial rings, introducing the concept of strongly ${\sigma}-IFP$ for a ring endomorphism ${\sigma}$. A ring R is said to have strongly ${\sigma}-IFP$ if the skew polynomial ring R[x;${\sigma}$] has IFP. We examine some characterizations and extensions of strongly ${\sigma}-IFP$ rings in relation with several ring theoretic properties which have important roles in ring theory. We also extend many of related basic results to the wider classes, and so several known results follow as consequences of our results.

• 대한수학회보
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• 제55권5호
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• pp.1389-1396
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• 2018

We observe the structure of a kind of unit-IFP ring that is constructed by Antoine, in relation with units and nilpotent elements. This article concerns the same argument in a more general situation, and study the structure of one-sided zero divisors in such rings. We also provide another kind of unit-IFP ring.

• 석유와에너지
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• 3호통권121호
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• pp.86-97
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• 1991

IFP(프랑스석유연구소)의 PJacqurd소장 및 D.Champlon 경제부장은 최근 Paris-Dauphine대학에서 개최된 「Energy:the end of crises?」라는 제하의 회의에서 기술진보의 석유매장량, 생산코스트, 석유공급등에의 영향에 관한 분석을 통해, 세계의 석유확인매장량이 증가하는 가운데 기술개발의 중요성은 조금도 감소되지 않고 있다는 발표를 하였다. 본고는 IFP의 간행물인 「Profil IFP」에 게재된 발표요지를 소개한 것이다.<편집자 주>

• 대한수학회지
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• 제55권5호
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• pp.1257-1268
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• 2018

In this article we first investigate a sort of unit-IFP ring by which Antoine provides very useful information to ring theory in relation with the structure of coefficients of zero-dividing polynomials. Here we are concerned with the whole shape of units and nilpotent elements in such rings. Next we study the properties of unit-IFP rings through group actions of units on nonzero nilpotent elements. We prove that if R is a unit-IFP ring such that there are finite number of orbits under the left (resp., right) action of units on nonzero nilpotent elements, then R satisfies the descending chain condition for nil left (resp., right) ideals of R and the upper nilradical of R is nilpotent.

• 대한수학회보
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• 제49권2호
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• pp.381-394
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• 2012

We generalize the insertion-of-factors-property by setting nilpotent products of elements. In the process we introduce the concept of a nil-IFP ring that is also a generalization of an NI ring. It is shown that if K$\ddot{o}$the's conjecture holds, then every nil-IFP ring is NI. The class of minimal noncommutative nil-IFP rings is completely determined, up to isomorphism, where the minimal means having smallest cardinality.