• Communications of the Korean Mathematical Society
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• v.31 no.4
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• pp.657-665
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• 2016

In this investigation we studied completely quasi primary and weakly completely quasi primary ideals in ternary semirings. Some characterizations of completely quasi primary and weakly completely quasi primary ideals were obtained. Moreover, we investigated relationships between completely quasi primary and weakly completely quasi primary ideals in ternary semirings. Finally, we obtained necessary and sufficient conditions for a weakly completely quasi primary ideal to be a completely quasi primary ideal.

• Journal of the Korean Mathematical Society
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• v.54 no.2
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• pp.675-684
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• 2017

Let G be a group with identity e and let R be a G-graded ring. In this paper, we introduce and study graded 2-absorbing primary and graded weakly 2-absorbing primary ideals of a graded ring which are different from 2-absorbing primary and weakly 2-absorbing primary ideals. We give some properties and characterizations of these ideals and their homogeneous components.

• Bulletin of the Korean Mathematical Society
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• v.57 no.5
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• pp.1205-1213
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• 2020

Let R be a commutative ring with 1 ≠ 0. In this paper, we introduce a subclass of the class of 1-absorbing primary ideals called the class of strongly 1-absorbing primary ideals. A proper ideal I of R is called strongly 1-absorbing primary if whenever nonunit elements a, b, c ∈ R and abc ∈ I, then ab ∈ I or c ∈ ${\sqrt{0}}$. Firstly, we investigate basic properties of strongly 1-absorbing primary ideals. Hence, we use strongly 1-absorbing primary ideals to characterize rings with exactly one prime ideal (the UN-rings) and local rings with exactly one non maximal prime ideal. Many other results are given to disclose the relations between this new concept and others that already exist. Namely, the prime ideals, the primary ideals and the 1-absorbing primary ideals. In the end of this paper, we give an idea about some strongly 1-absorbing primary ideals of the quotient rings, the polynomial rings, and the power series rings.

• Health Policy and Management
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• v.9 no.2
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• pp.139-156
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• 1999

Recent changes in the health care environment have directed increasing attention to the number and specialty mix of practicing physicians. A major concern identified in Korean health care system is the serious oversupply of specialists and a relative lack of primary care physicians. Currently only 21% of Korean physicians are primary care physicians(general practitioners and family physicians), and less than 10% of recent medical school graduates are choosing to enter primary care. More primary care physicians are needed to deal with major problems in the current health care system, such as cost and access. The infrastructure that relies on primary care physicians is needed to deliver cost-effective and efficient care. To achieve a better balance of primary care to non-primary care physicians. more medical students need to choose careers in one of the primary care specialties(family medicine. internal medicine and pediatrics). This paper suggests the necessity of reforming the Korean graduate medical education system, that is, establishing the path of training primary care physicians in internal medicine and pediatrics residency training programs.

• Kyungpook Mathematical Journal
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• v.57 no.4
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• pp.559-580
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• 2017

Let G be an arbitrary group with identity e and let R be a G-graded ring. In this paper, we define the concept of graded 2-absorbing and graded weakly 2-absorbing primary ideals of commutative G-graded rings with non-zero identity. A number of results and basic properties of graded 2-absorbing primary and graded weakly 2-absorbing primary ideals are given.

• East Asian mathematical journal
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• v.29 no.1
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• pp.101-107
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• 2013

We consider a cognitive network with a primary and a secondary channel. Primary users have higher priority on the usage of the primary channel, and secondary users are allowed to opportunistically access the primary channel at times when the channel is not occupied by primary users. The secondary channel is dedicated only to secondary users. An analytical model is presented to obtain the performance of an opportunistic spectrum access using both the primary and secondary channels, and is validated by simulations.

• Journal of the korean academy of Pediatric Dentistry
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• v.4 no.1
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• pp.7-18
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• 1977

The author carried out to determine the normal range of eruptive time, average age and order of eruption of primary teeth in korean infants. The examimation was given to 1757 healty infants(Male 1032, female 725) from afterbirth 4 months to 32 months. The results was as fallows. 1. The eruption of primary teeth was 0.57 months earlier in male than in female. 2. The average month of eruption of primary teeth was as follows; Upper primary central is $9.66{\pm}0.19$ months Upper primary lateral is $11.58{\pm}0.18$ months. Upper primary canine is $18.06{\pm}0.32$ months. Upper first primary molar is $16.45{\pm}0.29$ months. Upper second primary molar is $24.28{\pm}0.51$ months. Lower primary central is $7.50{\pm}0.12$ months. Lower primary lateral is $12.87{\pm}0.16$ months. Lower primary camine is $18.82{\pm}0.34$ months. Lower first primary molar is $17.66{\pm}0.37$ months. Lower second primary molar is $23.89{\pm}0.51$ months. 3. The eruptive order of the korean is different from that of the American and same to that of Japanese. 4. There is no significant right and left arch. 5. Generally, the eruption of primary teeth on the upper is 1.08 months earlier than on the lower; but the upper central is 2.16 months later than the lower and the upper second primary is 0.39 months later than the lower.

• Honam Mathematical Journal
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• v.29 no.4
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• pp.631-640
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• 2007

In this paper, we introduce the notions of intuitionistic fuzzy w-primary submodule and intuitionistic fuzzy w-primary ideal. And we give an example of intuitionistic fuzzy w-primary submodule and some related properties are investigated.

• Bulletin of the Korean Mathematical Society
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• v.58 no.5
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• pp.1069-1078
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• 2021

Let R be a commutative ring with identity. A proper ideal I of R is called 1-absorbing primary ([4]) if for all nonunit a, b, c ∈ R such that abc ∈ I, then either ab ∈ I or c ∈ ${\sqrt{1}}$. The concept of 1-absorbing primary ideals in a polynomial ring, in a PID and in idealization of a module is studied. Moreover, we introduce weakly 1-absorbing primary ideals which are generalization of weakly prime ideals and 1-absorbing primary ideals. A proper ideal I of R is called weakly 1-absorbing primary if for all nonunit a, b, c ∈ R such that 0 ≠ abc ∈ I, then either ab ∈ I or c ∈ ${\sqrt{1}}$. Some properties of weakly 1-absorbing primary ideals are investigated. For instance, weakly 1-absorbing primary ideals in decomposable rings are characterized. Among other things, it is proved that if I is a weakly 1-absorbing primary ideal of a ring R and 0 ≠ I₁I₂I₃ ⊆ I for some ideals I₁, I₂, I₃ of R such that I is free triple-zero with respect to I₁I₂I₃, then I₁I₂ ⊆ I or I₃ ⊆ I.

• Bulletin of the Korean Mathematical Society
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• v.56 no.3
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• pp.729-743
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• 2019

In this paper, we introduce strongly quasi primary ideals which is an intermediate class of primary ideals and quasi primary ideals. Let R be a commutative ring with nonzero identity and Q a proper ideal of R. Then Q is called strongly quasi primary if $ab{\in}Q$ for $a,b{\in}R$ implies either $a^2{\in}Q$ or $b^n{\in}Q$ ($a^n{\in}Q$ or $b^2{\in}Q$) for some $n{\in}{\mathbb{N}}$. We give many properties of strongly quasi primary ideals and investigate the relations between strongly quasi primary ideals and other classical ideals such as primary, 2-prime and quasi primary ideals. Among other results, we give a characterization of divided rings in terms of strongly quasi primary ideals. Also, we construct a subgraph of ideal based zero divisor graph ${\Gamma}_I(R)$ and denote it by ${\Gamma}^*_I(R)$, where I is an ideal of R. We investigate the relations between ${\Gamma}^*_I(R)$ and ${\Gamma}_I(R)$. Further, we use strongly quasi primary ideals and ${\Gamma}^*_I(R)$ to characterize von Neumann regular rings.