• Journal of applied mathematics & informatics
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• v.33 no.3_4
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• pp.469-474
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• 2015

In this paper, we will consider the notions of (m, n)-potent conditions in near-rings, in particular, a near-ring R with left bipotent or right bipotent condition. We will derive some properties of near-rings with (1, n) and (n, 1)-potent conditions where n is a positive integer, and then some properties of near-rings with (m, n)-potent conditions. Also, we may discuss the behavior of R-subgroups in (1, n)-potent or (n, 1)-potent near-rings..

• Bulletin of the Korean Mathematical Society
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• v.57 no.1
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• pp.37-50
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• 2020

Linear complementary dual (LCD) codes are linear codes that intersect with their dual trivially. LCD cyclic codes have been known as reversible cyclic codes that had applications in data storage. Due to a newly discovered application in cryptography, interest in LCD codes has increased again. Although LCD codes over finite fields have been extensively studied so far, little work has been done on LCD codes over chain rings. In this paper, we are interested in structure of LCD codes over chain rings. We show that LCD codes over chain rings are free codes. We provide some necessary and sufficient conditions for an LCD code C over finite chain rings in terms of projections of linear codes. We also showed the existence of asymptotically good LCD codes over finite chain rings.

• Bulletin of the Korean Mathematical Society
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• v.54 no.1
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• pp.51-69
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• 2017

We, in this paper, study the commutativity of skew polynomials at zero as a generalization of an ${\alpha}-rigid$ ring, introducing the concept of strongly skew reversibility. A ring R is be said to be strongly ${\alpha}-skew$ reversible if the skew polynomial ring $R[x;{\alpha}]$ is reversible. We examine some characterizations and extensions of strongly ${\alpha}-skew$ reversible rings in relation with several ring theoretic properties which have roles in ring theory.

• Bulletin of the Korean Mathematical Society
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• v.56 no.1
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• pp.57-71
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• 2019

Let R be an associative ring with identity, M a t.u.p. monoid with only one unit and ${\omega}:M{\rightarrow}End(R)$ a monoid homomorphism. Let R be a reversible, M-compatible ring and ${\alpha}=a_1g_1+{\cdots}+a_ng_n$ a non-zero element in skew monoid ring $R{\ast}M$. It is proved that if there exists a non-zero element ${\beta}=b_1h_1+{\cdots}+b_mh_m$ in $R{\ast}M$ with ${\alpha}{\beta}=c$ is a constant, then there exist $1{\leq}i_0{\leq}n$, $1{\leq}j_0{\leq}m$ such that $g_{i_0}=e=h_{j_0}$ and $a_{i_0}b_{j_0}=c$ and there exist elements a, $0{\neq}r$ in R with ${\alpha}r=ca$. As a consequence, it is proved that ${\alpha}{\in}R*M$ is unit if and only if there exists $1{\leq}i_0{\leq}n$ such that $g_{i_0}=e$, $a_{i_0}$ is unit and aj is nilpotent for each $j{\neq}i_0$, where R is a reversible or right duo ring. Furthermore, we determine the relation between clean and nil clean elements of R and those elements in skew monoid ring $R{\ast}M$, where R is a reversible or right duo ring.

• Journal of the Korean Mathematical Society
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• v.53 no.2
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• pp.381-401
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• 2016

According to Jacobson [31], a right ideal is bounded if it contains a non-zero ideal, and Faith [15] called a ring strongly right bounded if every non-zero right ideal is bounded. From [30], a ring is strongly right AB if every non-zero right annihilator is bounded. In this paper, we introduce and investigate a particular class of McCoy rings which satisfy Property (A) and the conditions asked by Nielsen [42]. It is shown that for a u.p.-monoid M and ${\sigma}:M{\rightarrow}End(R)$ a compatible monoid homomorphism, if R is reversible, then the skew monoid ring R * M is strongly right AB. If R is a strongly right AB ring, M is a u.p.-monoid and ${\sigma}:M{\rightarrow}End(R)$ is a weakly rigid monoid homomorphism, then the skew monoid ring R * M has right Property (A).

• Communications of the Korean Mathematical Society
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• v.35 no.2
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• pp.447-454
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• 2020

The studies of reversible and NI rings have done important roles in noncommutative ring theory. A ring R shall be called QRUR if ab = 0 for a, b ∈ R implies that ba is contained in the upper nilradical of R, which is a generalization of the NI ring property. In this article we investigate the structure of QRUR rings and examine the QRUR property of several kinds of ring extensions including matrix rings and polynomial rings. We also show that if there exists a weakly semicommutative ring but not QRUR, then Köthe's conjecture does not hold.

• Bulletin of the Korean Mathematical Society
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• v.54 no.6
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• pp.1913-1925
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• 2017

Let R be a ring with identity. An ideal N of R is called ideal-symmetric (resp., ideal-reversible) if $ABC{\subseteq}N$ implies $ACB{\subseteq}N$ (resp., $AB{\subseteq}N$ implies $BA{\subseteq}N$) for any ideals A, B, C in R. A ring R is called ideal-symmetric if zero ideal of R is ideal-symmetric. Let S(R) (called the ideal-symmetric radical of R) be the intersection of all ideal-symmetric ideals of R. In this paper, the following are investigated: (1) Some equivalent conditions on an ideal-symmetric ideal of a ring are obtained; (2) Ideal-symmetric property is Morita invariant; (3) For any ring R, we have $S(M_n(R))=M_n(S(R))$ where $M_n(R)$ is the ring of all n by n matrices over R; (4) For a quasi-Baer ring R, R is semiprime if and only if R is ideal-symmetric if and only if R is ideal-reversible.

• The Journal of Korean Medicine
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• v.19 no.2
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• pp.228-243
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• 1998

This study was undertaken to evaluate the effect of Sunghyangchungisan (SHCS) on the regulation of vascular tone. Vascular rings isolated from rabbit carotid artery were myographed isometrically in isolated organ baths and the effect of SHCS on contractile activities were determined. SHCS relaxed the arterial rings which were pre-contracted by phenylephrine(PE). The responses to SHCS were partially dose-dependent at concentrations lower than 0.5 mg/ml. When SHCS was applied prior to the exposure to PE, it inhibited the PE-induced contraction by a similar magnitude which was comparable to the relaxation of pre-contracted arterial rings. Washout of SHCS after observing its relaxant effect resulted in a full recovery of PE-induced contractions, indicating that the action mechanism is reversible. The observation that SHCS did not change the $ED_{50}$ of PE on its dose-response curve ruled out the possible interaction of SHCS and ${\alpha}-receptor$. The relaxant effect of SHCS was not affected by removal of endothelium, and pretreatment of the arterial rings with methylene blue or nitro-L-arginine. This results suggest that the action of SHCS is not mediated by endothelium nor soluble guanylate cyclase. SHCS relaxed high $K^{+}-induced$ contractions as well, whereas it failed to relax phorbol ester-induced contractions. When contraction was induced by additive application of $Ca^{2+}$ in arterial rings which were pre-depolarized by high $K^+$ in a $Ca^{2+}-free$ solution, the relaxant effect of SHCS was attenuated by increasing the $Ca^{2+}$ concentration. SHCS, when applied to the arterial rings pre-contracted by PE and then relaxed by nifedipine, a $Ca^{2+}$ channel blocker, did not show additive relaxation. From above results, it is suggested that SHCS relax PE-induced contraction of rabbit carotid artery in an endothelium-independent manner, and inhibition of $Ca^{2+}$ influx may contribute to the underling mechanism.

• The Journal of Internal Korean Medicine
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• v.21 no.3
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• pp.377-388
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• 2000

Objective : This study was undertaken to evaluate the effect of Sunghyangchungisan (SHCS) on the regulation of vascular tone and $Ca^{2+}$ metabolism in arterial tissues. Vascular rings isolated from rabbit carotid artery were myographed isometrically in isolated organ baths and the effect of SHCS on contractile activities, endothelial function and $Ca^{2+}$ metabolism were determined. Methods : In phentobarbital sodium-anesthetized rabbits, SHCS administered through ear vein (100 mg/Kg body wt.) or intragastric dwelling tube (300 mg/Kg body wt.) attenuated phenylephrine (PE, 10 ${\mu}g$/Kg, i.v.)-induced increases in both systolic and diastolic cartoid arterial blood pressure. Results : In experiments with isolated arterial strips, SHCS relaxed arterial rings which were pre-contracted by phenylephrine (PE, 1 ${\mu}M$). The responses to SHCS were partially dose-dependent at concentrations lower than 0.5 mg/ml. When SHCS was applied prior to the exposure to PE, it inhibited the PE-induced contraction by a similar magnitude which was comparable to the relaxation of pre-contracted arterial rings. Washout of SHCS after observing its relaxant effect resulted in a full recovery of PE-induced contractions, indicating that the action mechanism is reversible. The observation that SHCS did not change the $ED_{50)$ of PE oh its dose-response curve ruled out the possible interaction of SHCS with ${\alpha}$-receptors. The relaxant effect of SHCS was not affected by removal of endothelium or a nitric oxide synthase inhibitor, L-NAME. Methylene blue, an inhibitor of the soluble guanylate cyclase, did not affect the relaxant effect of SHCS. These results suggest that the action of SHCS is not mediated by the endothelium nor soluble guanylate cyclase. Constant cGMP production determined in arterial strips in the presence or absence of SHCS is consistent with this conclusion. When contraction was induced by additive application of $Ca^{2+}$ in arterial rings which were pre-depolarized by high $K^+$ in a $Ca^{2+}$-free solution, the relaxant effect of SHCS was attenuated by increasing the $Ca^{2+}$ concentration. SHCS, when applied to the arterial rings pre-contracted by PE and then relaxed by nifedipine, a $Ca^{2+}$ channel blocker, did not show additive relaxation. SHCS partially blocked $Ca^{2+}$ influx stimulated by PE and high $K^+$ which was determined by 5-min ^{45}Ca$ uptake, while it did not affect $Ca^{2+}$ efflux. Conclusions : From above results, it is suggested that SHCS relax PE-induced contraction of rabbit carotid artery in an endothelium independent manner, andinhibition of $Ca^{2+}$ influx may contribute to the underling mechanism.

• Bulletin of the Korean Mathematical Society
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• v.55 no.3
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• pp.921-935
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• 2018

In this study we determine the structure of m-adic residue codes over the non-chain ring $F_q[v]/(v^2-v)$ and present some promising examples of such codes that have optimal parameters with respect to Griesmer Bound. Further, we show that the generators of m-adic residue codes serve as a natural and suitable application for generating reversible DNA codes via a special automorphism and sets over $F_{4^{2k}}[v]/(v^2-v)$.