• East Asian mathematical journal
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• v.38 no.1
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• pp.1-12
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• 2022

Let R be a ring with an endomorphism σ and a σ-derivation δ. R is called (σ, δ)-Baer (resp. (σ, δ)-quasi-Baer, (σ, δ)-p.q.-Baer, (σ, δ)-p.p.) if the right annihilator of every right (σ, δ)-set (resp., (σ, δ)-ideal, principal (σ, δ)-ideal, (σ, δ)-element) of R is generated by an idempotent of R. In this paper, for a given Ore extension A = R[x; σ, δ] of R, the following properties are investigated: If R is a σ-rigid ring in which σ and δ commute, then (1) R is (σ, δ)-Baer if and only if R is (σ, δ)-quasi-Baer if and only if A is (${\bar{\sigma}},\;{\bar{\delta}}$)-Baer if and only if A is (${\bar{\sigma}},\;{\bar{\delta}}$)-quasi-Baer; (2) R is (σ, δ)-p.p. if and only if R is (σ, δ)-p.q.-Baer if and only if A is (${\bar{\sigma}},\;{\bar{\delta}}$)-p.p. if and only if A is (${\bar{\sigma}},\;{\bar{\delta}}$)-p.q.-Baer.

• Bulletin of the Korean Mathematical Society
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• v.45 no.1
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• pp.59-66
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• 2008

Keskin and Harmanci defined the family B(M,X) = ${A{\leq}M|{\exists}Y{\leq}X,{\exists}f{\in}Hom_R(M,X/Y),\;Ker\;f/A{\ll}M/A}$. And Orhan and Keskin generalized projective modules via the class B(M, X). In this note we introduce X-local summands and X-hollow modules via the class B(M, X). Let R be a right perfect ring and let M be an X-lifting module. We prove that if every co-closed submodule of any projective module P contains Rad(P), then M has an indecomposable decomposition. This result is a generalization of Kuratomi and Chang's result [9, Theorem 3.4]. Let X be an R-module. We also prove that for an X-hollow module H such that every non-zero direct summand K of H with $K{\in}B$(H, X), if $H{\oplus}H$ has the internal exchange property, then H has a local endomorphism ring.

• 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.

• 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.

• Journal of the Korean Mathematical Society
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• v.46 no.1
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• pp.51-58
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• 2009

Let R be a ring. A right R-module M is called perfect if M possesses a projective cover. In this paper, we consider the relationship between the class of perfect modules and other classes of modules. Some known rings are characterized by these relationships.

• Bulletin of the Korean Mathematical Society
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• v.54 no.4
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• pp.1281-1291
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• 2017

Let R be a strongly 2-primal ring and I a proper ideal of R. Then there are only finitely many prime ideals minimal over I if and only if for every prime ideal P minimal over I, the ideal $P/{\sqrt{I}}$ of $R/{\sqrt{I}}$ is finitely generated if and only if the ring $R/{\sqrt{I}}$ satisfies the ACC on right annihilators. This result extends "D. D. Anderson, A note on minimal prime ideals, Proc. Amer. Math. Soc. 122 (1994), no. 1, 13-14." to large classes of noncommutative rings. It is also shown that, a 2-primal ring R only has finitely many minimal prime ideals if each minimal prime ideal of R is finitely generated. Examples are provided to illustrate our results.

• Korean Journal of Clinical Pharmacy
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• v.21 no.1
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• pp.6-13
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• 2011

Bolus intravenous injection of adenosine resulted the temporal decrease of systemic blood pressure and heart rate in the anesthetized rats. Adenosine also resulted the persistent decrease of contractility and heart rate in the isolated spontaneously beating rat right atria. Both of the above inhibition effets of adenosine were increased by the pretreatment of NBI (nitrobenzylthioinosine), whitch is an adenosine transport inhibitor, but decreased by the pretreatment of 8- phenyltheophy1line, which is an adenosine antagonist. In isolated thoracic aorta ring segment of normotensive rats, intact rings were relaxed by adenosine ($42.3{\pm}8.7%$) and ATP ($85.9{\pm}15.8%$) in the concentration of $10^{-4}M$, but rubbed rings were relaxed by adenosine ($35.2{\pm}1.9%$) and ATP ($11.3{\pm}9.0%$) in $10^{-4}M$. After pretreatment of L-NAME (N-Nitro-Larginine methyl ester), which is an NO inhibitor, adenosine-induced relaxation was not affected, but ATP-induced relax ation was significantly inhibited (P<0.01). Meanwhile, adenosine resulted almost same as vasorelaxation in isolated thoracic aorta of SHR comparing to those of normotensive rats. But, vasodilation responses of ATP in intact rings of SHR are significantly inhibited comparing to those of normotensive rats. Adenosine-induced relaxation is attenuated after 8-phenyltheophylline pretreatment, but increased after NBI pretreatment. However, ATP-induced relaxations are not affected by 8-phenyltheophylline or NBI pretreatment. These results suggested that the hypotensive effects of adenosine was due to the decrease of contractile force and heart rate through the A1 receptor and vasodilation are mediated by A2 receptor of the vascular smooth muscle. And, the heart protective and vasodilation effects of adenosine might suggest that it would be useful in the acute treatment of coronary artery disease.

• Bulletin of the Korean Mathematical Society
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• v.55 no.2
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• pp.573-586
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• 2018

Let R be a noncommutative prime ring of characteristic different from 2, Q be its maximal right ring of quotients and C be its extended centroid. Suppose that $f(x_1,{\ldots},x_n)$ be a noncentral multilinear polynomial over $C,b{\in}Q,F$ a b-generalized derivation of R and d is a nonzero derivation of R such that d([F(f(r)), f(r)]) = 0 for all $r=(r_1,{\ldots},r_n){\in}R^n$. Then one of the following holds: (1) there exists ${\lambda}{\in}C$ such that $F(x)={\lambda}x$ for all $x{\in}R$; (2) there exist ${\lambda}{\in}C$ and $p{\in}Q$ such that $F(x)={\lambda}x+px+xp$ for all $x{\in}R$ with $f(x_1,{\ldots},x_n)^2$ is central valued in R.

• Korean Journal of Ichthyology
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• v.23 no.1
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• pp.30-36
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• 2011

Age and growth of shotted halibut Eopsetta grigorjewi were estimated using right sagittal otoliths of 389 fish specimens from February 2004 to January 2005 in the East China Sea. Examination of outer margins of the otolith showed that the opaque zone was formed once a year and annual rings were formed from December to March. The age of specimens examined ranged from 3 to 5 years. Shotted halibut begin spawning in February and show a peak in March. Length and weight relationships showed no significant difference between females and males (P>0.05), and can be expressed as TW=$0.5091{\times}10^{-2}TL^{3,222}(r^2=0.92)$. Estimated von Bertalanffy growth curve was $L_t=46.58(1-e^{-0.14(1+1.32)})$.

• Korean Journal of Fisheries and Aquatic Sciences
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• v.44 no.6
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• pp.689-694
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• 2011

Age and growth of whitespotted conger Conger myriaster were estimated using right sagittal otoliths from 495 fish collected from February, 2004, to January, 2005, in the southern coastal waters of Korea. Examination of the outer margin of the otoliths showed that opaque zones formed once a year and annual rings formed from April to June. The ages of the specimens examined ranged from 3 to 8 years. Whitespotted conger spawn from December to March. Allometry between preanal length and total weight can be expressed as $TW=0.0350{\times}PL^{2.9173}$ ($R^2=0.89$). There was no significant difference in allometry between females and males (P>0.05). The estimated VBF growth equation was $L_t=415.2(1-e^{-0.1457(t+0.4654)})$.