• Journal of the Korean Mathematical Society
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• v.60 no.6
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• pp.1233-1254
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• 2023

We introduce two subclasses of abelian McCoy rings, so-called π-CN-rings and π-duo rings, and systematically study their fundamental characteristic properties accomplished with relationships among certain classical sorts of rings such as 2-primal rings, bounded rings etc. It is shown that a ring R is π-CN whenever every nilpotent element of index 2 in R is central. These rings naturally generalize the long-known class of CN-rings, introduced by Drazin [9]. It is proved that π-CN-rings are abelian, McCoy and 2-primal. We also show that, π-duo rings are strongly McCoy and abelian and also they are strongly right AB. If R is π-duo, then R[x] has property (A). If R is π-duo and it is either right weakly continuous or every prime ideal of R is maximal, then R has property (A). A π-duo ring R is left perfect if and only if R contains no infinite set of orthogonal idempotents and every left R-module has a maximal submodule. Our achieved results substantially improve many existing results.

• Bulletin of the Korean Mathematical Society
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• v.39 no.3
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• pp.411-422
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• 2002

In this note we are concerned with relationships between one-sided ideals and two-sided ideals, and study the properties of polynomial rings whose maximal one-sided ideals are two-sided, in the viewpoint of the Nullstellensatz on noncommutative rings. Let R be a ring and R[x] be the polynomial ring over R with x the indeterminate. We show that eRe is right quasi-duo for $0{\neq}e^2=e{\in}R$ if R is right quasi-duo; R/J(R) is commutative with J(R) the Jacobson radical of R if R[$\chi$] is right quasi-duo, from which we may characterize polynomial rings whose maximal one-sided ideals are two-sided; if R[x] is right quasi-duo then the Jacobson radical of R[x] is N(R)[x] and so the $K\ddot{o}the's$ conjecture (i.e., the upper nilradical contains every nil left ideal) holds, where N(R) is the set of all nilpotent elements in R. Next we prove that if the polynomial rins R[x], over a reduced ring R with $\mid$X$\mid$ $\geq$ 2, is right quasi-duo, then R is commutative. Several counterexamples are included for the situations that occur naturally in the process of this note.

• Communications of the Korean Mathematical Society
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• v.37 no.2
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• pp.399-407
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• 2022

In this paper, we continue to study the von Neumann regularity of rings whose essential maximal right ideals are GP-injective. It is proved that the following statements are equivalent: (1) R is strongly regular; (2) R is a 2-primal ring whose essential maximal right ideals are GP-injective; (3) R is a right (or left) quasi-duo ring whose essential maximal right ideals are GP-injective. Moreover, it is shown that R is strongly regular if and only if R is a strongly right (or left) bounded ring whose essential maximal right ideals are GP-injective. Finally, we prove that a PI-ring whose essential maximal right ideals are GP-injective is strongly π-regular.

• Bulletin of the Korean Mathematical Society
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• v.40 no.2
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• pp.223-234
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• 2003

This note contains the following results for a ring A : (1) A is simple Artinian if and only if A is a prime right YJ-injective, right and left V-ring with a maximal right annihilator ; (2) if A is a left quasi-duo ring with Jacobson radical J such that $_{A}$A/J is p-injective, then the ring A/J is strongly regular ; (3) A is von Neumann regular with non-zero socle if and only if A is a left p.p.ring containing a finitely generated p-injective maximal left ideal satisfying the following condition : if e is an idempotent in A, then eA is a minimal right ideal if and only if Ae is a minimal left ideal ; (4) If A is left non-singular, left YJ-injective such that each maximal left ideal of A is either injective or a two-sided ideal of A, then A is either left self-injective regular or strongly regular : (5) A is left continuous regular if and only if A is right p-injective such that for every cyclic left A-module M, $_{A}$M/Z(M) is projective. ((5) remains valid if 《continuous》 is replaced by 《self-injective》 and 《cyclic》 is replaced by 《finitely generated》. Finally, we have the following two equivalent properties for A to be von Neumann regula. : (a) A is left non-singular such that every finitely generated left ideal is the left annihilator of an element of A and every principal right ideal of A is the right annihilator of an element of A ; (b) Change 《left non-singular》 into 《right non-singular》in (a).(a).

• Journal of the Korean Mathematical Society
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• v.55 no.5
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• pp.1193-1205
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• 2018

We focus our attention on a ring property that nilpotents are contained in the Jacobson radical. This property is satisfied by NI and left (right) quasi-duo rings. A ring is said to be NJ if it satisfies such property. We prove the following: (i) $K{\ddot{o}}the^{\prime}s$ conjecture holds if and only if the polynomial ring over an NI ring is NJ; (ii) If R is an NJ ring, then R is exchange if and only if it is clean; and (iii) A ring R is NJ if and only if so is every (one-sided) corner ring of R.

• MALSORI
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• no.37
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• pp.23-48
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• 1999

To improve the performance of automatic labelling system, the context-dependent demiphone unit was proposed. A phone is divided into two parts: a left demiphone that accounts for the left side coarticulation and a right demiphone that copes with the right side context. Demiphone unit provides a better training of the transition between phones. In this paper, If the length of the phone is less than 120 msec, it is split into two demiphones. If the length of the phone is greater than 120 msec, it is divided into three parts. In order to evaluate the performance of the system, we use 452 phonetically balanced words(PBW) database for training and testing phoneme models. According to the experiment, the system using proposed demiphone unit compared with that using old demiphone unit gains 3.83% improved result(71.63%) within 10ms of the duo boundary, and 2.20% improved result(86.41%) within 20ms of the true boundary.

• Honam Mathematical Journal
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• v.35 no.4
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• pp.583-606
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• 2013

We generalize the idea of (${\in}$, ${\in}{\vee}q_k$)-fuzzy ordered semi-group and give the concept of (${\in}$, ${\in}{\vee}q_k$)-fuzzy ordered $\mathcal{LA}$-semigroup. We show that (${\in}$, ${\in}{\vee}q_k$)-fuzzy left (right, two-sided) ideals, (${\in}$, ${\in}{\vee}q_k$)-fuzzy (generalized) bi-ideals, (${\in}$, ${\in}{\vee}q_k$)-fuzzy interior ideals and (${\in}$, ${\in}{\vee}q_k$)-fuzzy (1, 2)-ideals need not to be coincide in an ordered $\mathcal{LA}$-semigroup but on the other hand, we prove that all these (${\in}$, ${\in}{\vee}q_k$)-fuzzy ideals coincide in a left regular class of an ordered $\mathcal{LA}$-semigroup. Further we investigate some useful conditions for an ordered $\mathcal{LA}$-semigroup to become a left regular ordered $\mathcal{LA}$-semigroup and characterize a left regular ordered $\mathcal{LA}$-semigroup in terms of (${\in}$, ${\in}{\vee}q_k$)-fuzzy one-sided ideals. Finally we connect an ideal theory with an (${\in}$, ${\in}{\vee}q_k$)-fuzzy ideal theory by using the notions of duo and (${\in}{\vee}q_k$)-fuzzy duo.

• Journal of the Korean Mathematical Society
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• v.57 no.3
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• pp.793-807
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• 2020

Stable range of rings is a unifying concept for problems related to the substitution and cancellation of modules. The newly appeared element-wise setting for the simplest case of stable range one is tempting to study the lifting property modulo ideals. We study the lifting of elements having (idempotent) stable range one from a quotient of a ring R modulo a two-sided ideal I by providing several examples and investigating the relations with other lifting properties, including lifting idempotents, lifting units, and lifting of von Neumann regular elements. In the case where the ring R is a left or a right duo ring, we show that stable range one elements lift modulo every two-sided ideal if and only if R is a ring with stable range one. Under a mild assumption, we further prove that the lifting of elements having idempotent stable range one implies the lifting of von Neumann regular elements.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.8 no.1
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• pp.269-281
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• 2014

Compared to hiding information into digital image, hiding information into digital text file requires less storage space and smaller bandwidth for data transmission, and it has obvious universality and extensiveness. However, text files have low redundancy, so it is more difficult to hide information in text files. To overcome this difficulty, Wang et al. proposed a reversible information hiding scheme using left-right and up-down representations of Chinese characters, but, when the scheme is implemented, it does not provide good visual steganographic effectiveness, and the embedding and extracting processes are too complicated to be done with reasonable effort and cost. We observed that a lot of traditional and simplified Chinese characters look somewhat the same (also called lookalike), so we utilize this feature to propose a novel information hiding scheme for hiding secret data in lookalike Chinese characters. Comparing to Wang et al.'s scheme, the proposed scheme simplifies the embedding and extracting procedures significantly and improves the effectiveness of visual steganographic images. The experimental results demonstrated the advantages of our proposed scheme.

• Journal of Nutrition and Health
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• v.6 no.1
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• pp.53-69
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• 1973

For the purpose of ascertaining the status of physical growth and development of the University students, an intensive survey was conducted by the authors towards a total of 2,197 (male: 1,694, female: 503) who passed the written enterance examination at the Korea University in 1972. The items included the measurements on physical growth, various physical indices, status of visual distourbance and pulmonary infiltration. The findings and results can be summarized as follows. 1. Physical growth: The average of body height by sex were 167.2 cm in male and 156.0cm in female, body weight 59.3kg and 51.9kg, chest-girth 86.7cm and 81.2cm, sitting height 91.7cm and 85.8cm, respectively. 2. Various indices about physical growth & development; Relative body weight by sex were 35.47 and 33.27, relative chest girth 51.85 and 52.05, relative sitting height 54.84 and 55.00, respectively. $R{\ddot{a}}here$ index was 1,269 in males and 1,367 in females, Kaup index 2,121 and 2,133, Verveck index 87.32 and 85.32, respectively. 3. Status of visual distaurbance: The vision of the students under 0.9 with Han's testing chart was 52.83% and 55.27% in left eye and 53.60% and 54.87% in right eye, respectively. 4. Pulmonary infiltration Among the total 58 students were diagncsed as pulmonary infiltration (tuberculosis), of whom 43 were minimal case, 12 were moderately advanced cases and 3 were far advanced cases.