• Journal of the Korean Mathematical Society
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• v.9 no.1
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• pp.31-34
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• 1972

• Korean Journal of Environmental Biology
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• v.40 no.4
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• pp.477-496
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• 2022

During a survey of free-living marine nematodes of Korea, two new marine desmoscolecid nematodes belonging to subgenus Quadricoma Filipjev, 1922 were discovered. Tricoma (Q.) jejuensis sp. nov. and T.(Q.) unipapillata sp. nov. are described based on specimens obtained from washings of coarse sediments from eastern and southern coasts of Korea. Tricoma (Q.) jejuensis sp. nov. is characterized by having 33 quadricomoid body rings and inversion at main ring 23, pentagonal head with truncated anterior end, a pair of ocelli situated at main ring 6, somatic setae comprising of 8 pairs of subdorsal setae and 12 pairs of subventral setae, and relatively short spicules (42-46 ㎛ long). Tricoma (Q.) unipapillata sp. nov. is characterized by 44 quadricomoid body rings and inversion at main ring 32, somatic setae comprising of 7 pairs of subdorsal setae and 10 pairs of subventral setae, globular head truncated anterior end, relatively short and stumpy cephalic setae with cuticular flange, one single naked ventral median genital papillae situated on main ring 20, and spicules with a proximally marked capitulum. Detailed morphological descriptions and illustrations of these two new species are provided in this study.

• Journal of the Korean Mathematical Society
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• v.42 no.1
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• pp.53-63
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• 2005

Let R be a ring R and ${\sigma}$ be an endomorphism of R. R is called ${\sigma}$-rigid (resp. reduced) if $a{\sigma}r(a) = 0 (resp{\cdot}a^2 = 0)$ for any $a{\in}R$ implies a = 0. An ideal I of R is called a ${\sigma}$-ideal if ${\sigma}(I){\subseteq}I$. R is called ${\sigma}$-quasi-Baer (resp. right (or left) ${\sigma}$-p.q.-Baer) if the right annihilator of every ${\sigma}$-ideal (resp. right (or left) principal ${\sigma}$-ideal) of R is generated by an idempotent of R. In this paper, a skew polynomial ring A = R[$x;{\sigma}$] of a ring R is investigated as follows: For a ${\sigma}$-rigid ring R, (1) R is ${\sigma}$-quasi-Baer if and only if A is quasi-Baer if and only if A is $\={\sigma}$-quasi-Baer for every extended endomorphism $\={\sigma}$ on A of ${\sigma}$ (2) R is right ${\sigma}$-p.q.-Baer if and only if R is ${\sigma}$-p.q.-Baer if and only if A is right p.q.-Baer if and only if A is p.q.-Baer if and only if A is $\={\sigma}$-p.q.-Baer if and only if A is right $\={\sigma}$-p.q.-Baer for every extended endomorphism $\={\sigma}$ on A of ${\sigma}$.

• Bulletin of the Korean Mathematical Society
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• v.42 no.1
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• pp.45-51
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• 2005

In this paper, we establish necessary and sufficient conditions for an exchange ideal to be a qb-ideal. It is shown that an exchange ideal I of a ring R is a qb-ideal if and only if when-ever $a{\simeq}b$ via I, there exists u ${\in} I_q^{-1}$ such that a = $ubu_q^{-1}$ and b = $u_q^{-1}$. This gives a generalization of the corresponding result of exchange QB-rings.

• Journal of the Chungcheong Mathematical Society
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• v.7 no.1
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• pp.33-39
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• 1994

The purpose of this paper prove the following property; Suppose A has many units (local global ring) and |A/m| > 5 for every maximal ideal $m{\subseteq}A$. Let(E, q) ${\in}$ Q(A) and $E=E_1{\bot}{\cdots}{\bot}E_t$ be an orthogonl decomposition of E with $t{\geq}2$ and $rk(E_i){\geq}1$, for $i=1,{\cdots},t$. Let $x{\in}E$ be a primitive vector. Then there exists ${\sigma}{\in}O(q)$ such that ${\sigma}(x)$ is transversal to this decomposition.

• Communications of the Korean Mathematical Society
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• v.25 no.3
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• pp.349-364
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• 2010

P. M. Cohn called a ring R reversible if whenever ab = 0, then ba = 0 for a, $b\;{\in}\;R$. Commutative rings and reduced rings are reversible. In this paper, we extend the reversible condition of a ring as follows: Let R be a ring and $\alpha$ an endomorphism of R, we say that R is right (resp., left) $\alpha$-shifting if whenever $a{\alpha}(b)\;=\;0$ (resp., $\alpha{a)b\;=\;0$) for a, $b\;{\in}\;R$, $b{\alpha}{a)\;=\;0$ (resp., $\alpha(b)a\;=\;0$); and the ring R is called $\alpha$-shifting if it is both left and right $\alpha$-shifting. We investigate characterizations of $\alpha$-shifting rings and their related properties, including the trivial extension, Jordan extension and Dorroh extension. In particular, it is shown that for an automorphism $\alpha$ of a ring R, R is right (resp., left) $\alpha$-shifting if and only if Q(R) is right (resp., left) $\bar{\alpha}$-shifting, whenever there exists the classical right quotient ring Q(R) of R.

• Bulletin of the Korean Mathematical Society
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• v.50 no.5
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• pp.1501-1511
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• 2013

A ring R is called linearly McCoy if whenever linear polynomials $f(x)$, $g(x){\in}R[x]{\backslash}\{0\}$ satisfy $f(x)g(x)=0$, there exist nonzero elements $r,s{\in}R$ such that $f(x)r=sg(x)=0$. In this paper, extension properties of linearly McCoy rings are investigated. We prove that the polynomial ring over a linearly McCoy ring need not be linearly McCoy. It is shown that if there exists the classical right quotient ring Q of a ring R, then R is right linearly McCoy if and only if so is Q. Other basic extensions are also considered.

• Kyungpook Mathematical Journal
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• v.57 no.3
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• pp.419-431
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• 2017

In this paper, we define a new kind of formal power series rings by using Gaussian binomial coefficients and investigate some properties. More precisely, we call such a ring a Gaussian series ring and study McCoy's theorem, Hermite properties and Noetherian properties.

• Bulletin of the Korean Mathematical Society
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• v.29 no.1
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• pp.101-116
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• 1992

• Animal Systematics, Evolution and Diversity
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• no.nspc5
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• pp.61-70
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• 2005

A new marine interstitial nematode species belonging to the subgenus Quadricoma of order Desmoscolecida is described from Jindo Island, South Korea. The new species, Tricoma (Quadricoma) jindoensis sp. nov., is most allied with T. (Q.) crassicomoides Timm, 1970 in sharing the similar cephalic setae, broadly truncated border of head, lip region including 6 labial papillae, and slender and long spicule among the seven congeners with 44 quadricomoid rings. However, T. (Q.) jindoensis differs from it by the globular protuberance on the penultimate ring, 7 tail rings, and 9 pairs of subdorsal setae in male. This is the first record of Quadricoma nematodes from East Asia.