• Bulletin of the Korean Mathematical Society
• /
• v.48 no.2
• /
• pp.277-290
• /
• 2011

We show that the ${\theta}$-prime radical of a ring R is the set of all strongly ${\theta}$-nilpotent elements in R, where ${\theta}$ is an automorphism of R. We observe some conditions under which the ${\theta}$-prime radical of coincides with the prime radical of R. Moreover we characterize elements in prime radicals of skew Laurent polynomial rings, studying (${\theta}$, ${\theta}^{-1}$)-(semi)primeness of ideals of R.

• Bulletin of the Korean Mathematical Society
• /
• v.55 no.4
• /
• pp.1103-1107
• /
• 2018

Let M be a complete spacelike hypersurface in the (n + 1)-dimensional Minkowski space ${\mathbb{L}}^{n+1}$. Suppose that every unit speed curve X(s) on M satisfies ${\langle}X^{\prime\prime}(s),X^{\prime\prime}s){\rangle}{\geq}-1/r^2$ and there exists a point $p{\in}M$ such that for every unit speed geodesic X(s) of M through the point p, ${\langle}X^{\prime\prime}(s),X^{\prime\prime}s){\rangle}=-1/r^2$ holds. Then, we show that up to isometries of ${\mathbb{L}}^{n+1}$, M is the hyperbolic space $H^n(r)$.

• Bulletin of the Korean Mathematical Society
• /
• v.57 no.5
• /
• pp.1177-1193
• /
• 2020

Fully prime rings (in which every proper ideal is prime) have been studied by Blair and Tsutsui, and fully semiprime rings (in which every proper ideal is semiprime) have been studied by Courter. For a given module M, we introduce the notions of a fully prime module and a fully semiprime module, and extend certain results of Blair, Tsutsui, and Courter to the category subgenerated by M. We also consider the relationship between the conditions (1) M is a fully prime (semiprime) module, and (2) the endomorphism ring of M is a fully prime (semiprime) ring.

• The Pure and Applied Mathematics
• /
• v.21 no.3
• /
• pp.147-163
• /
• 2014

In this paper, we study the existence of positive solutions for singular impulsive differential equations with integral boundary conditions $$\{u^{{\prime}{\prime}}(t)+q(t)f(t,u(t),u^{\prime}(t))=0,\;t{\in}\mathbb{J}^{\prime},\\{\Delta}u(t_k)=I_k(u(t_k),u^{\prime}(t_k)),\;k=1,2,{\cdots},p,\\{\Delta}u^{\prime}(t_k)=-L_k(u(t_k),u^{\prime}(t_k)),\;k=1,2,{\cdots},p,\\u=(0)={\int}_{0}^{1}g(t)u(t)dt,\;u^{\prime}=0,$$) where the nonlinearity f(t, u, v) may be singular at v = 0. The proof is based on the theory of Leray-Schauder degree, together with a truncation technique. Some recent results in the literature are generalized and improved.

• Kyungpook Mathematical Journal
• /
• v.56 no.1
• /
• pp.41-46
• /
• 2016

A graph G of order n has prime cordial labeling if its vertices can be assigned the distinct labels 1, $2{\cdots}$, n such that if each edge xy in G is assigned the label 1 in case the labels of x and y are relatively prime and 0 otherwise, then the number of edges labeled with 0 and the number of edges labeled with 1 differ by at most 1. In this paper, we give a complete characterization of complete graphs which are prime cordial and we give a prime cordial labeling of the closed helm ${\bar{H}}_n$, and present a new way of prime cordial labeling of $P^2_n$. Finally we make a correction of the proof of Theorem 2.5 in [12].

• International Journal of Fuzzy Logic and Intelligent Systems
• /
• v.12 no.3
• /
• pp.198-204
• /
• 2012

We introduce the notions of interval-valued fuzzy prime ideals, interval-valued fuzzy completely prime ideals and interval-valued fuzzy weakly completely prime ideals. And we give a characterization of interval-valued fuzzy ideals and establish relationships between interval-valued fuzzy completely prime ideals and interval-valued fuzzy weakly completely prime ideals.

• Kyungpook Mathematical Journal
• /
• v.59 no.1
• /
• pp.65-71
• /
• 2019

This paper is concerned with the existence of positive solutions of the nonlinear Neumann boundary value problems $$\{u^{{\prime}{\prime}}+a(t)u={\lambda}b(t)f(u),\;t{\in}(0,1),\\u^{\prime}(0)=u^{\prime}(1)=0$$, where $a,b{\in}C[0,1]$ with $a(t)>0,\;b(t){\geq}0$ and the Green's function of the linear problem $$\{u^{{\prime}{\prime}}+a(t)u=0,\;t{\in}(0,1),\\u^{\prime}(0)=u^{\prime}(1)=0$$ may change its sign on $[0,1]{\times}[0,1]$. Our analysis relies on the Leray-Schauder fixed point theorem.

• Bulletin of the Korean Mathematical Society
• /
• v.59 no.6
• /
• pp.1387-1408
• /
• 2022

Let R be a commutative ring with a non-zero identity, S be a multiplicatively closed subset of R and M be a unital R-module. In this paper, we define a submodule N of M with (N :_R M)∩S = ∅ to be weakly S-prime if there exists s ∈ S such that whenever a ∈ R and m ∈ M with 0 ≠ am ∈ N, then either sa ∈ (N :_R M) or sm ∈ N. Many properties, examples and characterizations of weakly S-prime submodules are introduced, especially in multiplication modules. Moreover, we investigate the behavior of this structure under module homomorphisms, localizations, quotient modules, cartesian product and idealizations. Finally, we define two kinds of submodules of the amalgamation module along an ideal and investigate conditions under which they are weakly S-prime.

• Bulletin of the Korean Mathematical Society
• /
• v.61 no.3
• /
• pp.717-734
• /
• 2024

Let R be a commutative ring with identity and m, n be positive integers. In this paper, we introduce the class of weakly (m, n)-prime ideals generalizing (m, n)-prime and weakly (m, n)-closed ideals. A proper ideal I of R is called weakly (m, n)-prime if for a, b ∈ R, 0 ≠ a^mb ∈ I implies either aⁿ ∈ I or b ∈ I. We justify several properties and characterizations of weakly (m, n)-prime ideals with many supporting examples. Furthermore, we investigate weakly (m, n)-prime ideals under various contexts of constructions such as direct products, localizations and homomorphic images. Finally, we discuss the behaviour of this class of ideals in idealization and amalgamated rings.

• Journal of Sasang Constitutional Medicine
• /
• v.7 no.1
• /
• pp.281-293
• /
• 1995

In order to investigate the effects of the $So{\breve{u}}m$-In $Sipj{\breve{o}}ndaebot^{\prime}ang$ and the Gukbang $Sipj{\breve{o}}ndaebot^{\prime}ang$ on Yang-insufficient syndrome(陽虛)induced by hydrocortisone acetate and cold condition in experiemental animals(Rats), the author experimented with Body temperature, Body weight, Exercise time, cyclic-AMP and Hair conditions. The results were obtained as follows ; 1. In Changes of body Temperature, the soum-In $Sipj{\breve{o}}ndaebot^{\prime}ang$ group rose with statistical significance in comparison to the controlled group, and the Soum-In $Sipj{\breve{o}}ndaebot^{\prime}ang$ treated group rose with statistical singificance in comparison to the Gukbang $Sipj{\breve{o}}ndaebot^{\prime}ang$ treated group. 2. In changes of Body weight, the Soum-In Sipjondaebot'ang treated group and the Gukbang Sipjondabot'ang treatd group had increased with statistical significance in comparison to the controlled group, and the $So{\breve{u}}m$-In $Sipj{\breve{o}}ndaebot^{\prime}ang$ treated group showed an increasing tendency in comparison to the Gukbang $Sipj{\breve{o}}ndaebot^{\prime}ang$treated group. 3. In changes of Exercise time, the $So{\breve{u}}m$-In $Sipj{\breve{o}}ndaebot^{\prime}ang$ treated group and the Gukbang $Sipj{\breve{o}}ndaebot^{\prime}ang$ treated group had increased with statistical significance in comparison to the controlled group and the $So{\breve{u}}m$ $Sipj{\breve{o}}ndaebot^{\prime}ang$ treated group showed an increasing tendency in comparison to the Gukbang $Sipj{\breve{o}}ndaebot^{\prime}ang$ treated group. 4. In changes of plasma cyclic-AMP concentration, the Gukbang $Sipj{\breve{o}}ndaebot^{\prime}ang$ treated group and the $So{\breve{u}}m$ $Sipj{\breve{o}}ndaebot^{\prime}ang$ treated group showed an increased tendency in comparison to the controlled group. 5. In changes hair condition, the $So{\breve{u}}m$ $Sipj{\breve{o}}ndaebot^{\prime}ang$ terated group and the Gukbang $Sipj{\breve{o}}ndaebot^{\prime}ang$ treated group showed a betterment tendency in comparison to the controlled group. From the above findings, thd $So{\breve{u}}m$ $Sipj{\breve{o}}ndaebot^{\prime}ang$ and the Gukbang $Sipj{\breve{o}}ndaebot^{\prime}ang$ groups also had an effect of Yang-insuffient syndrome, moreover, on Body thmperature, Body weight and Exercise time, both showed a singnificant effect.