• Communications of the Korean Mathematical Society
• /
• v.37 no.2
• /
• pp.399-407
• /
• 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
• /
• v.47 no.3
• /
• pp.611-622
• /
• 2010

A ring R is called left max-coherent provided that every maximal left ideal is finitely presented. $\mathfrak{M}\mathfrak{I}$ (resp. $\mathfrak{M}\mathfrak{F}$) denotes the class of all max-injective left R-modules (resp. all max-flat right R-modules). We prove, in this article, that over a left max-coherent ring every right R-module has an $\mathfrak{M}\mathfrak{F}$-preenvelope, and every left R-module has an $\mathfrak{M}\mathfrak{I}$-cover. Furthermore, it is shown that a ring R is left max-injective if and only if any left R-module has an epic $\mathfrak{M}\mathfrak{I}$-cover if and only if any right R-module has a monic $\mathfrak{M}\mathfrak{F}$-preenvelope. We also give several equivalent characterizations of MI-injectivity and MI-flatness. Finally, $\mathfrak{M}\mathfrak{I}$-dimensions of modules and rings are studied in terms of max-injective modules with the left derived functors of Hom.

• Bulletin of the Korean Mathematical Society
• /
• v.35 no.3
• /
• pp.455-464
• /
• 1998

In this paper, we give another proof of Theorem 2.13 of [4] without using the sup property. For the homomorphic image $f(\mu)$ and preimage $f^{-1}(\nu)$ of fuzzy left (resp. right) ideals $\mu$ and $\nu$ respectively, we establish the chains of level left (resp. right) ideals of $f(\mu)$ and $f^{-1}(\nu)$, respectively. Moreover, we prove that a necessary condition for a fuzzy ideal $\mu$ of a near-ring $R$ to be prime is that $\mu$ is two-valued.

• Communications of the Korean Mathematical Society
• /
• v.30 no.3
• /
• pp.143-154
• /
• 2015

Characterizations of hesitant fuzzy left (right) ideals are considered. The notion of hesitant fuzzy (generalized) bi-ideals is introduced, and related properties are investigated. Relations between hesitant fuzzy generalized bi-ideals and hesitant fuzzy semigroups are discussed, and characterizations of (hesitant fuzzy) generalized bi-ideals and hesitant fuzzy bi-ideals are considered. Given a hesitant fuzzy set $\mathcal{H}$ on a semigroup S, hesitant fuzzy (generalized) bi-ideals generated by $\mathcal{H}$ are established.

• Journal of the Korean Mathematical Society
• /
• v.51 no.3
• /
• pp.495-507
• /
• 2014

Nielsen and Rege-Chhawchharia called a ring R right McCoy if given nonzero polynomials f(x), g(x) over R with f(x)g(x) = 0, there exists a nonzero element r ${\in}$ R with f(x)r = 0. Hong et al. called a ring R strongly right McCoy if given nonzero polynomials f(x), g(x) over R with f(x)g(x) = 0, f(x)r = 0 for some nonzero r in the right ideal of R generated by the coefficients of g(x). Subsequently, Kim et al. observed similar conditions on linear polynomials by finding nonzero r's in various kinds of one-sided ideals generated by coefficients. But almost all results obtained by Kim et al. are concerned with the case of products of linear polynomials. In this paper we examine the nonzero annihilators in the products of general polynomials.

• Korean Journal of Applied Biomechanics
• /
• v.14 no.1
• /
• pp.145-160
• /
• 2004

The purposes of this study to provide quantitative data in necessary to advance techniques kinematic analysis of Cucarachas which is an action of Rumba. Then, this study is performed on 5 female players who have won within the third prize at a national athletic meeting. When whole foot reached to floor, Displacement of right-left hip joint (until $E1{\sim}E3$ average moved 15.15cm)is found at right-left direction since the hip joint is turned to right back. On the other side, large displacement is shown because Rumba Cucaracha Movement is expressed by maximum shift of hip joint to right and left direction. Displacement of right hip joint(E3$57.40{\pm}7.46$) is found in front and in rear direction since hip joint is moved in rear and in front to turn the hip joint. It may be stated that this is ideal displacement expressed by movement of whole body with artistic poise and presentation because role of hip joint is very important in technical and artistic side. Angle of right shoulder joint E2($105.44{\pm}9.64$) is got wider. It may be stated that player shifts up and abduct elbow joint to right since center of gravity of player is exceedingly shifted to right in this motion of Cucarachas. On the other hand, since this motion is abducted right elbow and shrunk external abdominal oblique to him center of body to left front of hip joint, the angle becomes narrow. It is shown that angle of knee in right knee joint E4($75.44{\pm}2.61$) is large since right leg and hip joint is turned by foot using reaction of ground and so center of body is shifted to left. Large angle of ankle E4($134.40{\pm}10.50$) in Cucaracha Movement is shown by the action of twist force using narrow part of foot and compression force against ground with adduction speed of arm. The various kinematic analyses associated with motions of dance sport have not been sufficiently peformed so far, and thus a number of research projects for dance sport should be proposed and performed to be continuous.

• The Pure and Applied Mathematics
• /
• v.1 no.1
• /
• pp.1-6
• /
• 1994

In this paper, some properties for a PI-ring satisfying the descending chain condition on essential left ideals are studied: Let R be a ring with a polynomial identity satisfying the descending chain condition on essential ideals. Then all minimal prime ideals in R are maximal ideals. Moreover, if R has only finitely many minimal prime ideals, then R is left and right Artinian. Consequently, if every primeideal of R is finitely generated as a left ideal, then R is left and right Artinian. A finitely generated PI-algebra over a commutative Noetherian ring satisfying the descending chain condition on essential left ideals is a finite module over its center.(omitted)

• Korean Journal of Mathematics
• /
• v.21 no.2
• /
• pp.171-180
• /
• 2013

We consider a fuzzy semigroup S in a right (or left) reductive semigroup X such that $S(k)=1$ for some $k{\in}X$ and find a faithful representation (or anti-representation) of S by transformations of S. Also we show that a fuzzy semigroup S in a weakly reductive semigroup X such that $S(k)=1$ for some $k{\in}X$ is isomorphic to the semigroup consisting of all pairs of inner right and left translations of S and that S can be embedded into the semigroup consisting of all pairs of linked right and left translations of S with the property that S is an ideal of the semigroup.

• Communications of the Korean Mathematical Society
• /
• v.34 no.2
• /
• pp.415-427
• /
• 2019

Let R be an associative ring with nonzero identity. The annihilator ideal graph of R, denoted by ${\Gamma}_{Ann}(R)$, is a graph whose vertices are all nonzero proper left ideals and all nonzero proper right ideals of R, and two distinct vertices I and J are adjacent if $I{\cap}({\ell}_R(J){\cup}r_R(J)){\neq}0$ or $J{\cap}({\ell}_R(I){\cup}r_R(I)){\neq}0$, where ${\ell}_R(K)=\{b{\in}R|bK=0\}$ is the left annihilator of a nonempty subset $K{\subseteq}R$, and $r_R(K)=\{b{\in}R|Kb=0\}$ is the right annihilator of a nonempty subset $K{\subseteq}R$. In this paper, we assume that R is a semicommutative ring. We study the structure of ${\Gamma}_{Ann}(R)$. Also, we investigate the relations between the ring-theoretic properties of R and graph-theoretic properties of ${\Gamma}_{Ann}(R)$. Moreover, some combinatorial properties of ${\Gamma}_{Ann}(R)$, such as domination number and clique number, are studied.

• Journal of Korean Physical Therapy Science
• /
• v.7 no.2
• /
• pp.615-628
• /
• 2000

This report is to study on the progress on which foot arch and planta has been changed according to body type based on 4 tilting of scapular & ilium. This study has been carried out to help contribute to some basic information like these. One was to find out how to assess and analysize the deformity of feet and ankle joint which may have the most impact on ideal alignment of anatomical posture. The other was to figure out how to diagnose and treat the deformity to get to the restoration. The results of this study is as followings; 1. The findings which had been made from 22 persons(50%) having left scapular and ilium forward tilt are as follows. 1) On the longitudinal length of the planta left parts of 18 persons(82%) are longer than the right one. On the transversel length of the planta right parts of 17 persons(77%) are longer than the left one. 2) On the size of medial longitudinal arch the left parts of 20 persons(91%) are more wider than the right one. 3) On the sign of supinated foot, the left parts of 18 persons(82%) are more common than the right one. 4) On the thickness of big toe, the left parts of 14 persons(64%) are thicker than the right one. 2. The findings which had been made from 15 persons(34%) having right scapular and ilium forward tilt are as follows. 1) On the longitudinal length of the planta right parts of 11 persons(73%) are longer than the left one. On the transversel length of the planta left parts of 13 persons(87%) are longer than the right one. 2) On the size of medial longitudinal arch the right parts of 13 persons(87%) are more wider than the left one. 3) On the sign of supinated foot, the right parts of 12 persons(80%) are more common than the left one. 4) On the thickness of big toe, the right parts of 7 persons(47%) are thicker than the left one. 3. The findings which had been made from 3 persons(7%) having left scapular and right ilium forward tilt are as follows. 1) On the longitudinal length of the planta right parts of 2 persons(67%) are longer than the left one. On the transversel length of the planta left parts of 2 persons(67%) are longer than the right one. 2) On the size of medial longitudinal arch the right parts of 3 persons(100%) are more wider than the left one. 3) On the sign of supinated foot, the right parts of 2 persons(67%) are more common than the left one. 4) On the thickness of big toe, the left parts of 2 persons(67%) are thicker than the right one. 4. The findings which had been made from 4 persons(9%) having right scapular and left ilium forward tilt are as follows. 1) On the longitudinal length of the planta left parts of 3 persons(75%) are longer than the right one. On the transversel length of the planta right parts of 2 persons(50%) are longer than the left one. 2) On the size of medial longitudinal arch the left parts of 3 persons(75%) are more wider than the right one. 3) On the sign of supinated foot, the left parts of 3 persons(75%) are more common than the right one. 4) On the thickness of big toe, the left parts of 3 persons(75%) are thicker than the right one.