• Kyungpook Mathematical Journal
• /
• v.57 no.2
• /
• pp.193-198
• /
• 2017

In this paper we investigate 2-absorbing ${\delta}$-primary ideals which unify 2-absorbing ideals and 2-absorbing primary ideals. A number of results about 2-absorbing ideals and 2-absorbing primary ideals are extended into this general framework.

• Bulletin of the Korean Mathematical Society
• /
• v.33 no.3
• /
• pp.445-453
• /
• 1996

A closed subspace J of a Banach space X is called an M-ideal in X if the annihilator $J^\perp$ of J is an L-summand of $X^*$. That is, there exists a closed subspace J' of $X^*$ such that $X^* = J^\perp \oplus J'$ and $\left\$\mid$ p + q \right\$\mid$ = \left\$\mid$ p \right\$\mid$ + \left\$\mid$ q \right\$\mid$$ wherever $p \in J^\perp and q \in J'$.

• The Mathematical Education
• /
• v.31 no.2
• /
• pp.141-144
• /
• 1992

In this paper, some properties of p-injective ring is studied: The Jacobson radical of a pinjective ring which satisfies the ascending chain condition on essential left ideals is nilpotent. Also, the left singular ideal of a ring which satisfies the ascending chain condition on essential left ideals is nilpotent. Finally, we give an example which shows that a semiprime left p-injective ring such that every essential left ideal is two-sided is not necessarily to be strongly regular.egular.

• Honam Mathematical Journal
• /
• v.30 no.3
• /
• pp.513-519
• /
• 2008

Let (R, m) be a Noetherian local ring with maximal ideal m, E := $E_R$(R/m) and let I be an ideal of R. Let M and N be finitely generated R-modules. It is shown that $H^n_I(M,(H^n_I(N)^{\vee})){\cong}(M{\otimes}_RN)^{\vee}$ where grade(I, N) = n = $cd_i$(I, N). We also show that for n = grade(I, R), one has $End_R(H^n_I(P,R)^{\vee}){\cong}Ext^n_R(H^n_I(P,R),P^*)^{\vee}$.

• Journal of the Korean Association of Oral and Maxillofacial Surgeons
• /
• v.26 no.3
• /
• pp.229-237
• /
• 2000

According to the functional matrix theory, Delaire proposes that individual occlusal plane was determined by variable effects of teeth, maxilla, mandible, cranium, cranial base and soft tissue matrix including the orofacial musculature. and that there is the ideal occlusal plane determined by the most proper spatial position of maxilla and mandible, functionally and esthetically. This study was designed to find out the relation between Delaire's ideal occlusal plane and muscle activity of masticatory muscles in individuals who have normal maxillo-mandibular relationships. Lateral cephalometric radiographs were taken and his/her individual occlusal plane and ideal occlusal plane were analyzed with Delaire's architectural and structural craniofacial analytic method. For evaluation of muscle activities of masticatory muscles, electromyography of anterior temporal muscle, superficial masseter muscle, and anterior belly of digastric muscle was recorded in fifty Korean normal Angle class I occlusion individuals. According to the average value of ideal occlusal plane, fifty normal Angle class I occlusion individuals were classified into three groups: Ideal occlusal plane group(I group), hyperrotation group(I+ group) and hyporotation group(I- group). The result of this study was as follows: 1. The results of Delaire's architectural and structural craniofacial analysis of lateral cephalography of the fifty Korean normal Angle class I occlusion individuals are that twelve persons(24%) have consistent or parallel with ideal occlusal plane and the average of angular difference was $1.22^{\circ}{\pm}3.69^{\circ}$. 2. There is no significant difference in muscle activities of masticatory muscles during resting(p<0.05), but significant increases of muscle activity of ipsilateral anterior temporal and masseter muscle, contralateral anterior belly of digastric muscle during unilateral chewing and of anterior temporal and masseter muscle during bilateral clenching(p<0.05). 3. To find out the effect of the angular difference between Delaire's ideal occlusal plane and real occlusal plane to muscle activity, muscle activities of masticatory muscles were compared with three groups in each other; I group, I+ group and I- group. The results were no significant differences during resting, unilateral chewing and bilateral clenching.(p>0.05) 4. Although there is no significant differences of masticatory muscle activities among the three groups, the fact that increasing tendency of masseter muscle activity of ideal occlusal plane group(I+) than those of any other groups(I+ and I-) during bilateral clenching was noted. There is only the implication that occlusal plane makes some effects on masticatory muscle activities, espacially that of masseter muscle during bilateral clenching. In conclusion, the hypothesis that occlusal plane is one of the factors which affect the muscle activities of masticatory muscles and that anyone whose occlusal plane consistent with Delaire's ideal occlusal plane has an extraordinary functional advantage in masticatory muscle function cannot be proven with electromyography methods.

• Communications of the Korean Mathematical Society
• /
• v.17 no.2
• /
• pp.221-227
• /
• 2002

In this paper we will show that the followings ; (1) Let R be a regular local ring of dimension n. Then $A_{n-2}$(R) = 0. (2) Let R be a regular local ring of dimension n and I be an ideal in R of height 3 such that R/I is a Gorenstein ring. Then [I] = 0 in $A_{n-3}$(R). (3) Let R = V[[ $X_1$, $X_2$, …, $X_{5}$ ]]/(p+ $X_1$$^{t1}$ + $X_2$$^{t2}$ + $X_3$$^{t3}$ + $X_4$$^2$+ $X_{5}$ $^2$/), where p $\neq$2, $t_1$, $t_2$, $t_3$ are arbitrary positive integers and V is a complete discrete valuation ring with (p) = mv. Assume that R/m is algebraically closed. Then all the Chow group for R is 0 except the last Chow group.group.oup.

• Bulletin of the Korean Mathematical Society
• /
• v.46 no.6
• /
• pp.1051-1060
• /
• 2009

In this paper, we give topological properties of collection of prime ideals in 2-primal near-rings. We show that Spec(N), the spectrum of prime ideals, is a compact space, and Max(N), the maximal ideals of N, forms a compact $T_1$-subspace. We also study the zero-divisor graph $\Gamma_I$(R) with respect to the completely semiprime ideal I of N. We show that ${\Gamma}_{\mathbb{P}}$ (R), where $\mathbb{P}$ is a prime radical of N, is a connected graph with diameter less than or equal to 3. We characterize all cycles in the graph ${\Gamma}_{\mathbb{P}}$ (R).

• Investigative Magnetic Resonance Imaging
• /
• v.20 no.1
• /
• pp.44-52
• /
• 2016

Purpose: To quantitatively and qualitatively compare fat-suppressed MRI quality using iterative decomposition of water and fat with echo asymmetry and least-squares estimation (IDEAL) with that using frequency selective fat-suppression (FSFS) T2- and postcontrast T1-weighted fast spin-echo images of the head and neck at 3T. Materials and Methods: The study was approved by our Institutional Review Board. Prospective MR image analysis was performed in 36 individuals at a single-center. Axial fat suppressed T2- and postcontrast T1-weighted images with IDEAL and FSFS were compared. Visual assessment was performed by two independent readers with respect to; 1) metallic artifacts around oral cavity, 2) susceptibility artifacts around upper airway, paranasal sinus, and head-neck junction, 3) homogeneity of fat suppression, 4) image sharpness, 5) tissue contrast of pathologies and lymph nodes. The signal-to-noise ratios (SNR) for each image sequence were assessed. Results: Both IDEAL fat suppressed T2- and T1-weighted images significantly reduced artifacts around airway, paranasal sinus, and head-neck junction, and significantly improved homogeneous fat suppression in compared to those using FSFS (P < 0.05 for all). IDEAL significantly decreased artifacts around oral cavity on T2-weighted images (P < 0.05, respectively) and improved sharpness, lesion-to-tissue, and lymph node-to-tissue contrast on T1-weighted images (P < 0.05 for all). The mean SNRs were significantly improved on both T1- and T2-weighted IDEAL images (P < 0.05 for all). Conclusion: IDEAL technique improves image quality in the head and neck by reducing artifacts with homogeneous fat suppression, while maintaining a high SNR.

• Journal of applied mathematics & informatics
• /
• v.36 no.3_4
• /
• pp.237-244
• /
• 2018

Let ${\mathcal{H}}$ be an infinite dimensional separable Hilbert space with a fixed orthonormal base $\{e_1,e_2,{\cdots}\}$. Let L be the subspace lattice generated by the subspaces $\{[e_1],[e_1,e_2],[e_1,e_2,e_3],{\cdots}\}$ and let $Alg{\mathcal{L}}$ be the algebra of bounded operators which leave invariant all projections in ${\mathcal{L}}$. Let p and q be natural numbers (p < q). Let ${\mathcal{A}}$ be a linear manifold in $Alg{\mathcal{L}}$ such that $T_{(p,q)}=0$ for all T in ${\mathcal{A}}$. If ${\mathcal{A}}$ is a Lie ideal, then $T_{(p,p)}=T_{(p+1,p+1)}={\cdots}=T_{(q,q)}$ and $T_{(i,j)}=0$, $p{\eqslantless}i{\eqslantless}q$ and i < $j{\eqslantless}q$ for all T in ${\mathcal{A}}$.

• Communications of the Korean Mathematical Society
• /
• v.28 no.1
• /
• pp.79-85
• /
• 2013

The structure of a poset P with smallest element 0 is looked at from two view points. Firstly, with respect to the Zariski topology, it is shown that Spec(P), the set of all prime semi-ideals of P, is a compact space and Max(P), the set of all maximal semi-ideals of P, is a compact $T_1$ subspace. Various other topological properties are derived. Secondly, we study the semi-ideal-based zero-divisor graph structure of poset P, denoted by $G_I$ (P), and characterize its diameter.