• Journal of applied mathematics & informatics
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• v.39 no.5_6
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• pp.617-622
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• 2021

Let R be a commutative ring with identity, R[X] the polynomial ring over R and S a multiplicative subset of R. Let U = {f ∈ R[X] | f is monic} and let N = {f ∈ R[X] | c(f) = R}. In this paper, we show that if S is an anti-Archimedean subset of R, then R is an S-Noetherian ring if and only if R[X]_U is an S-Noetherian ring, if and only if R[X]_N is an S-Noetherian ring. We also prove that if R is an integral domain and R[X]_U is an S-principal ideal domain, then R is an S-principal ideal domain.

• East Asian mathematical journal
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• v.37 no.1
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• pp.33-40
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• 2021

We discuss the condition that if ab = 0 for elements a, b in a ring R then aIb = 0 for some essential ideal I of R. A ring with such condition is called IEIP. We prove that a ring R is IEIP if and only if Dn(R) is IEIP for every n ≥ 2, where Dn(R) is the ring of n by n upper triangular matrices over R whose diagonals are equal. We construct an IEIP ring that is not Abelian and show that a well-known Abelian ring is not IEIP, noting that rings with the insertion-of-factors-property are Abelian.

• Communications of the Korean Mathematical Society
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• v.39 no.2
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• pp.373-397
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• 2024

Lambek introduced the concept of symmetric rings to expand the commutative ideal theory to noncommutative rings. In this study, we propose an extension of symmetric rings called strongly α-symmetric rings, which serves as both a generalization of strongly symmetric rings and an extension of symmetric rings. We define a ring R as strongly α-symmetric if the skew polynomial ring R[x; α] is symmetric. Consequently, we provide proofs for previously established outcomes regarding symmetric and strongly symmetric rings, directly derived from the results we have obtained. Furthermore, we explore various properties and extensions of strongly α-symmetric rings.

• Journal of electromagnetic engineering and science
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• v.3 no.2
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• pp.104-110
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• 2003

A ring filter is proposed as a wide-banded filter. It consists of a ring and two short stubs, which are connected at 90$^{\circ}$ and 270$^{\circ}$ points of the ring. Since the termination impedance at 90$^{\circ}$ and 270$^{\circ}$ points of the ring and the characteristic impedance of the short stub have an effect on designing of it, the relation between them and bandwidths has been studied. Based on the study, two types of small-sized wideband CVT(constant VSWR-type impedance transformer)- and CCT(constant conductance-type impedance transformer)-ring filters are introduced, designed, simulated and one of two, a CCT -ring filter, is tested. The circumference of the ring can be reduced theoretically up to 60$^{\circ}$ and two of many cases having about 300$^{\circ}$ circumferences are simulated. The simulated results show more than 100 % fractional bandwidth, which can be obtained with more than 5 stages in conventional filter-design techniques. To test the designed CCT-ring filter, it has been fabricated in microstrip technology and the measured results show good agreement with the simulated ones, having more than 100 % fractional bandwidth.

• Korean Journal of Mathematics
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• v.18 no.2
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• pp.119-132
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• 2010

P. M. Cohn called a ring R reversible if whenever ab = 0, then ba = 0 for $a,b{\in}R$. In this paper, we study an extension of a reversible ring with its endomorphism. An endomorphism ${\alpha}$ of a ring R is called strong right (resp., left) reversible if whenever $a{\alpha}(b)=0$ (resp., ${\alpha}(a)b=0$) for $a,b{\in}R$, ba = 0. A ring R is called strong right (resp., left) ${\alpha}$-reversible if there exists a strong right (resp., left) reversible endomorphism ${\alpha}$ of R, and the ring R is called strong ${\alpha}$-reversible if R is both strong left and right ${\alpha}$-reversible. We investigate characterizations of strong ${\alpha}$-reversible rings and their related properties including extensions. In particular, we show that every semiprime and strong ${\alpha}$-reversible ring is ${\alpha}$-rigid and that for an ${\alpha}$-skew Armendariz ring R, the ring R is reversible and strong ${\alpha}$-reversible if and only if the skew polynomial ring $R[x;{\alpha}]$ of R is reversible.

• The Korean Journal of Cytopathology
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• v.13 no.2
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• pp.88-92
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• 2002

Scattered single cells or variable sized clusters of signet ring cells in the aspirated smears of breast lesions are almost exclusively associated with carcinoma. The signet ring cells are defined as those containing a prominent intracytoplasmic vacuole or amorphous cytoplasm diffusely dispersed with mucin. The primary signet ring cell carcinoma of the breast behaves more aggressively than carcinoma without signet ring cells. Therefore, it is very important to make a correct diagnosis of signet ring cell carcinoma. Fine needle aspiration cytology is useful for diagnosis of breast lesions Including signet ring cell carcinoma. We report two cases, which showed mostly signet ring cells in the aspirated smears of the breast. One case consisted of numerous individual signet ring cells and variable sized cell clusters in rather mucoid background. The tumor cells had abundant amorphous cytoplasm filled with dispersed mucin or occasionally mucin vacuoles(PAS +) and eccentric nuclei. The resected mass revealed mucinous carcinoma. The other showed the cytologic findings of low cellularity, and small loosely cohesive signet ring cell clusters with mild nuclear pleomorphism. It was confirmed as lobular signet ring cell carcinoma in the resected tumor.

• Journal of the Korean Mathematical Society
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• v.42 no.3
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• pp.457-470
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• 2005

Yu showed that every right (left) primitive factor ring of weakly right (left) duo rings is a division ring. It is not difficult to show that each weakly right (left) duo ring is abelian and has the classical right (left) quotient ring. In this note we first provide a left duo ring (but not weakly right duo) in spite of it being left Noetherian and local. Thus we observe conditions under which weakly one-sided duo rings may be two-sided. We prove that a weakly one-sided duo ring R is weakly duo under each of the following conditions: (1) R is semilocal with nil Jacobson radical; (2) R is locally finite. Based on the preceding case (1) we study a kind of composition length of a right or left Artinian weakly duo ring R, obtaining that i(R) is finite and $\alpha^{i(R)}R\;=\;R\alpha^{i(R)\;=\;R\alpha^{i(R)}R\;for\;all\;\alpha\;{\in}\;R$, where i(R) is the index (of nilpotency) of R. Note that one-sided Artinian rings and locally finite rings are strongly $\pi-regular$. Thus we also observe connections between strongly $\pi-regular$ weakly right duo rings and related rings, constructing available examples.

• Journal of Ecology and Environment
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• v.36 no.1
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• pp.31-38
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• 2013

Annual ring formation is considered a source of information to investigate the effects of environmental changes caused by temperature, air pollution, and acid rain on tree growth. A comparative investigation of annual ring growth of Cryptomeria japonica in relation to environmental changes was conducted at two sites in southern Korea (Haenam and Jangseong). Three wood disks from each site were collected from stems at breast height and annual ring growth was analyzed. Annual ring area at two sites increased over time (p > 0.05). Tree ring growth rate in Jangseong was higher than that in Haenam. Annual ring area increment in Jangseong was more strongly correlated with environmental variables than that in Haenam; annual ring growth increased with increasing temperature (p < 0.01) and a positive effect of $NO_2$ concentration on annual ring area (p < 0.05) could be attributed to nitrogen deposition in Jangseong. The correlation of annual ring growth increased with decreasing $SO_2$ and $CO_2$ concentrations (p < 0.01) in Jangseong. Variation in annual growth rings in Jangseong could be associated with temperature changes and N deposition. In Haenam, annual ring growth was correlated with $SO_2$ concentration (p < 0.01), and there was a negative relationship between precipitation pH and annual ring area (p < 0.01) which may reflect changes in nutrient cycles due to the acid rain. Therefore, the combined effects of increased $CO_2$, N deposition, and temperature on tree ring growth in Jangseong may be linked to soil acidification in this forest ecosystem. The interactions between air pollution ($SO_2$) and precipitation pH in Haenam may affect tree growth and may change nutrient cycles in this site. These results suggested that annual tree ring growth in Jangseong was more correlated with environmental variables than that in Haenam. However, the further growth of C. japonica forest at two sites is at risk from the long-term effects of acid deposition from fossil fuel combustion.

• Bulletin of the Korean Mathematical Society
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• v.59 no.3
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• pp.529-545
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• 2022

This article concerns a ring property that arises from combining one-sided duo factor rings and centers. A ring R is called right CIFD if R/I is right duo by some proper ideal I of R such that I is contained in the center of R. We first see that this property is seated between right duo and right π-duo, and not left-right symmetric. We prove, for a right CIFD ring R, that W(R) coincides with the set of all nilpotent elements of R; that R/P is a right duo domain for every minimal prime ideal P of R; that R/W(R) is strongly right bounded; and that every prime ideal of R is maximal if and only if R/W(R) is strongly regular, where W(R) is the Wedderburn radical of R. It is also proved that a ring R is commutative if and only if D₃(R) is right CIFD, where D₃(R) is the ring of 3 by 3 upper triangular matrices over R whose diagonals are equal. Furthermore, we show that the right CIFD property does not pass to polynomial rings, and that the polynomial ring over a ring R is right CIFD if and only if R/I is commutative by a proper ideal I of R contained in the center of R.

• Bulletin of the Korean Mathematical Society
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• v.55 no.3
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• pp.837-849
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• 2018

In this paper, we study the closedness such as seminomality and t-closedness, and Noetherian-like properties such as piecewise Noetherianness and Noetherian spectrum, of Hurwitz polynomial rings and Hurwitz series rings. To do so, we construct an isomorphism between a Hurwitz polynomial ring (resp., a Hurwitz series ring) and a factor ring of a polynomial ring (resp., a power series ring) in a countably infinite number of indeterminates.