• Kyungpook Mathematical Journal
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• v.57 no.4
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• pp.545-558
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• 2017

In this paper, we introduce generalised quasi-ideals in ordered ternary semigroups. Also, we define ordered m-right ideals, ordered (p, q)-lateral ideals and ordered n-left ideals in ordered ternary semigroups and studied the relation between them. Some intersection properties of ordered (m,(p, q), n)-quasi ideals are examined. We also characterize these notions in terms of minimal ordered (m,(p, q), n)-quasi-ideals in ordered ternary semigroups. Moreover, m-right simple, (p, q)-lateral simple, n-left simple, and (m,(p, q), n)-quasi simple ordered ternary semigroups are defined and some properties of them are studied.

• KOREAN JOURNAL OF CROP SCIENCE
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• v.34 no.s01
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• pp.16-25
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• 1989

A bioassay is a test system using a living organism (in whole or in part) to determine the presence or relative potency of chemical substances. The development and uses of bioassay are intimately linked to the discovery and characterization of the major classes of plant hormones. An application of this relationship is helpful for understanding the concept of plant hormones as well as the use of bioassay. And plant bioassay have been development and employed not only for the discovery and characterization of the biological activity of plant growth regulators but also have served several important secondary roles. The ideal bioassay should possess the characteristic of high specificity. great sensitivity. short response time, low cost and ease of obtaining plant material. acceptable ease of manipulation, and minimal space and equipment requirements.

• Journal of the Korean Mathematical Society
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• v.42 no.2
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• pp.203-222
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• 2005

Thompson series is a Hauptmodul for a genus zero group which lies between $\Gamma$o(N) and its normalizer in PSL2(R) ([1]). We construct explicit ring class fields over an imaginary quadratic field K from the Thompson series $T_g$($\alpha$) (Theorem 4), which would be an extension of [3], Theorem 3.7.5 (2) by using the Shimura theory and the standard results of complex multiplication. Also we construct various class fields over K, over a CM-field K (${\zeta}N + {\zeta}_N^{-1}$), and over a field K (${\zeta}N$). Furthermore, we find an explicit formula for the conjugates of Tg ($\alpha$) to calculate its minimal polynomial where $\alpha$ (${\in}{\eta}$) is the quotient of a basis of an integral ideal in K.

• Bulletin of the Korean Mathematical Society
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• v.53 no.1
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• pp.163-180
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• 2016

We study the structure of an arbitrary graded Lie triple system $\mathfrak{T}$ with restrictions neither on the dimension nor the base field. We show that $\mathfrak{T}$ is of the form $\mathfrak{T}=U+\sum_{j}I_j$ with U a linear subspace of the 1-homogeneous component $\mathfrak{T}_1$ and any $I_j$ a well described graded ideal of $\mathfrak{T}$, satisfying $[I_j,\mathfrak{T},I_k]=0$ if $j{\neq}k$. Under mild conditions, the simplicity of $\mathfrak{T}$ is characterized and it is shown that an arbitrary graded Lie triple system $\mathfrak{T}$ is the direct sum of the family of its minimal graded ideals, each one being a simple graded Lie triple system.

• Bulletin of the Korean Mathematical Society
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• v.49 no.4
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• pp.715-736
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• 2012

Brown provided a structure theorem for a class of perfect ideals of grade 3 with type ${\lambda}$ > 0. We introduced a skew-symmetrizable matrix to describe a structure theorem for complete intersections of grade 4 in a Noetherian local ring. We construct a class of perfect ideals I of grade 3 with type 2 defined by a certain skew-symmetrizable matrix. We present the Hilbert function of the standard $k$-algebras R/I, where R is the polynomial ring $R=k[v_0,v_1,{\ldots},v_m]$ over a field $k$ with indeterminates $v_i$ and deg $v_i=1$.

• Journal of the Korean Mathematical Society
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• v.51 no.3
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• pp.593-607
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• 2014

Let R be an I-semiring and S(R) be the set of all identity-summand elements of R. In this paper we introduce the total graph of R with respect to identity-summand elements, denoted by T(${\Gamma}(R)$), and investigate basic properties of S(R) which help us to gain interesting results about T(${\Gamma}(R)$) and its subgraphs.

• Korean Journal of Poultry Science
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• v.28 no.2
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• pp.165-172
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• 2001

Vaccination is one of the most important and cost-effective methods of preventing infectious diseases. Over the past decade, scientific in molecular biology and immunology have improved understanding of many diseases and led to the development of novel strategies for vaccination. An ideal vaccine would induce effective immunity specific for the type of infection, have long duration, require minimal or no boosters, have safety, would not induce adverse reaction, and be easy to administer. The desire to meet these criteria has resulted in the development of vaccines that do not depend on the use of the viable disease agent. It is not the intent of this review to give an extensive review of the field of vaccinology, but rather to address characteristics of conventional and genetically engineered vaccines.

• Honam Mathematical Journal
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• v.33 no.3
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• pp.419-424
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• 2011

Let D be an integral domain, Spec(D) the set of prime ideals of D, and X a subspace of the Zariski topology on Spec(D). We show that X is compact if and only if given any ideal I of D with $I{\nsubseteq}P$ for all $P{\in}X$, there exists a finitely generated idea $J{\subseteq}I$ such that $J{\nsubseteq}P$ for all $P{\in}X$. We also prove that if D = ${\cap}_{P{\in}X}D_P$ and if * is the star-operation on D induced by X, then X is compact if and only if * $_f$-Max(D) ${\subseteq}$X. As a corollary, we have that t-Max(D) is compact and that ${\mathcal{P}}$(D) = {P${\in}$ Spec(D)$|$P is minimal over (a : b) for some a, b${\in}$D} is compact if and only if t-Max(D) ${\subseteq}\;{\mathcal{P}}$(D).

• Journal of the Chungcheong Mathematical Society
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• v.32 no.1
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• pp.15-21
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• 2019

Let X be a reduced closed subscheme in ${\mathbb{P}}^n$ and $${\pi}_q:X{\rightarrow}Y={\pi}_q(X){\subset}{\mathbb{P}}^{n-1}$$ be an isomorphic projection from the center $q{\in}{\mathbb{P}}^n{\backslash}X$. Suppose that the minimal free presentation of $I_X$ is of the following form $$R(-3)^{{\beta}2,1}{\oplus}R(-4){\rightarrow}R(-2)^{{\beta}1,1}{\rightarrow}I_X{\rightarrow}0$$. In this paper, we prove that $H^1(I_X(k))=H^1(I_Y(k))$ for all $k{\geq}3$. This implies that Y is k-normal if and only if X is k-normal for $k{\geq}3$. Moreover, we also prove that reg(Y) ${\leq}$ max{reg(X), 4} and that $I_Y$ is generated by homogeneous polynomials of degree ${\leq}4$.

• Communications of the Korean Mathematical Society
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• v.36 no.1
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• pp.27-39
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• 2021

We discuss the condition that every nonzero right annihilator of an element contains a nonzero ideal, as a generalization of the insertion-of-factors-property. A ring with such condition is called right AP. We prove that a ring R is right AP if and only if Dn(R) is right AP for every n ≥ 2, where Dn(R) is the ring of n by n upper triangular matrices over R whose diagonals are equal. Properties of right AP rings are investigated in relation to nilradicals, prime factor rings and minimal order.