• East Asian mathematical journal
• /
• v.18 no.1
• /
• pp.15-20
• /
• 2002

We study the relationships between strongly prime ideals and completely prime ideals, concentrating on the connections among various radicals(prime radical, upper nilradical and generalized nilradical). Given a ring R, consider the condition: (*) nilpotent elements of R form an ideal in R. We show that a ring R satisfies (*) if and only if every minimal strongly prime ideal of R is completely prime if and only if the upper nilradical coincides with the generalized nilradical in R.

• Journal of applied mathematics & informatics
• /
• v.25 no.1_2
• /
• pp.551-562
• /
• 2007

This paper concerns a relationship between rough sets, intuitionistic fuzzy sets and ring theory. We consider a ring as a universal set and we assume that the knowledge about objects is restricted by an intuitionistic fuzzy ideal. We apply the notion of intutionistic fuzzy ideal of a ring for definitions of the lower and upper approximations in a ring. Some properties of the lower and upper approximations are investigated.

• Bulletin of the Korean Mathematical Society
• /
• v.40 no.3
• /
• pp.531-536
• /
• 2003

We discuss the roughness of $\Gamma$-subsemigroups and ideals/bi-ideals in $\Gamma$-semigroups.

• Kyungpook Mathematical Journal
• /
• v.51 no.3
• /
• pp.339-344
• /
• 2011

Let D be an integral domain with quotient field K, X be an indeterminate over D, and D[X] be the polynomial ring over D. A prime ideal Q of D[X] is called an upper to zero in D[X] if Q = fK[X] ${\cap}$ D[X] for some f ${\in}$ D[X]. In this paper, we study integral domains D such that every upper to zero in D[X] contains a prime element (resp., a primary element, a t-invertible primary ideal, an invertible primary ideal).

• Communications of the Korean Mathematical Society
• /
• v.34 no.1
• /
• pp.113-125
• /
• 2019

In this paper, we introduce the elimination ideal $I_D(G)$ associated to a simple finite graph G. We obtain the upper bound of Castelnuovo-Mumford regularity of elimination ideal for various classes of graphs.

• The Pure and Applied Mathematics
• /
• v.7 no.1
• /
• pp.33-40
• /
• 2000

We prove some characterization of rings with chain conditions in terms of fuzzy quotient rings and fuzzy ideals. We also show that a ring R is left Artinian if and only of the set of values of every fuzzy ideal on R is upper well-ordered.

• Journal of the Korean Mathematical Society
• /
• v.54 no.6
• /
• pp.1733-1757
• /
• 2017

Let $R={\oplus}_{{\alpha}{\in}{\Gamma}}R_{\alpha}$ be an integral domain graded by an arbitrary torsionless grading monoid ${\Gamma}$, ${\bar{R}}$ be the integral closure of R, H be the set of nonzero homogeneous elements of R, C(f) be the fractional ideal of R generated by the homogeneous components of $f{\in}R_H$, and $N(H)=\{f{\in}R{\mid}C(f)_v=R\}$. Let $R_H$ be a UFD. We say that a nonzero prime ideal Q of R is an upper to zero in R if $Q=fR_H{\cap}R$ for some $f{\in}R$ and that R is a graded UMT-domain if each upper to zero in R is a maximal t-ideal. In this paper, we study several ring-theoretic properties of graded UMT-domains. Among other things, we prove that if R has a unit of nonzero degree, then R is a graded UMT-domain if and only if every prime ideal of $R_{N(H)}$ is extended from a homogeneous ideal of R, if and only if ${\bar{R}}_{H{\backslash}Q}$ is a graded-$Pr{\ddot{u}}fer$ domain for all homogeneous maximal t-ideals Q of R, if and only if ${\bar{R}}_{N(H)}$ is a $Pr{\ddot{u}}fer$ domain, if and only if R is a UMT-domain.

• Honam Mathematical Journal
• /
• v.39 no.1
• /
• pp.93-100
• /
• 2017

Let $\mathcal{H}$ be an infinite dimensional separable Hilbert space with a fixed orthonormal base $\{e_1,e_2,{\cdots}\}$. Let $\mathcal{L}$ 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($p{\leqslant}q$). Let $\mathcal{B}_{p,q}=\{T{\in}Alg\mathcal{L}{\mid}T_{(p,q)}=0\}$. Let $\mathcal{A}$ be a linear manifold in $Alg{\mathcal{L}}$ such that $\{0\}{\varsubsetneq}{\mathcal{A}}{\subset}{\mathcal{B}}_{p,q}$. If $\mathcal{A}$ is an ideal in $Alg{\mathcal{L}}$, then $T_{(i,j)}=0$, $p{\leqslant}i{\leqslant}q$ and $i{\leqslant}j{\leqslant}q$ for all T in $\mathcal{A}$.

• Journal of Fashion Business
• /
• v.20 no.4
• /
• pp.15-35
• /
• 2016

The purpose of this study was to develop brassiere pattern designed to fit the breast shapes based on ESMOD pattern. It has three quarters cup round shape and also consists of three parts; upper cup, lower cup, and wings. Breast types are classified into five shapes; ideal breast, flat breast, upper developed breast, lower developed breast, and projecting breast. Two subjects for each breast type wore the brassiere, and they evaluated the appearance and wearing twice. Type I for research pattern designed to fit into the breast shape reflecting details of breast size were assessed as superior to the divided commercial type. However, wings' tightness of Type I for research pattern brassiere was high. Thus, to improve wearing satisfaction, extra was added to wing. Based on the results of wearing experiments of Type I for research, we adjusted and modified Type II for research pattern. Subsequently, its appearance and wearing were evaluated, in order to be improved. For upper developed breast pattern, we extended the length of lower part to balance upper and lower part, as the upper part was somewhat long. The lower developed breast has the closest feature to the ideal breast, suggestive that implies it does not require much improvement Projecting breast pattern has minimal space in the lower part, so we added the support to lift them to be similar to the ideal breasts. For all the breast shapes, we reduced the wings' tightness from 8% to 7% so that we could extend the length of the wings.

• Kyungpook Mathematical Journal
• /
• v.52 no.4
• /
• pp.483-494
• /
• 2012

In this paper we study properties of commutative BE-algebras and we give the construction of quotient (X/I; *, I) of a commutative BE-algebra X via an obstinate ideal I of X. We construct upper semilattice and prove that is a nearlattice. Finally we define and study commutative ideals in BE-algebras.