• Kyungpook Mathematical Journal
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• v.60 no.1
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• pp.53-69
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• 2020

Let (A, M) ⊂ (B, N) be commutative quasi-local rings. We consider the property that there exists a ring D such that A ⊆ D ⊂ B and the extension D ⊂ B is inert. Examples show that the number of such D may be any non-negative integer or infinite. The existence of such D does not imply M ⊆ N. Suppose henceforth that M ⊆ N. If the field extension A/M ⊆ B/N is algebraic, the existence of such D does not imply that B is integral over A (except when B has Krull dimension 0). If A/M ⊆ B/N is a minimal field extension, there exists a unique such D, necessarily given by D = A + N (but it need not be the case that N = MB). The converse fails, even if M = N and B/M is a finite field.

• Journal of applied mathematics & informatics
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• v.40 no.3_4
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• pp.765-767
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• 2022

The inverse Galois problem concerns whether or not every finite group appears as the Galois group of some Galois extension of the rational numbers. This problem, first posed in the early 19th century, is unsolved. In other words, we consider a pair - the group G and the field K. The question is whether there is an extension field L of K such that G is the Galois group of L. In this paper we present the proof that any group G is a Galois group of any field extension. In other words, we only consider the group G. And we present the solution to the inverse Galois problem.

• Journal of Agricultural Extension & Community Development
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• v.2 no.2
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• pp.109-116
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• 1995

The objectives of this study were to identify the roles of field agricultural extension work and its future development directions in the localization process. Literature reviews and participatory research methods were applied to attain the study objectives. Among the identified developmental roles of the field extension work in the localization process were : (1) to build up the agricultural research capability within the locality ; (2) to intensify the field information technology and ; (3) to strengthen the technology management capability of the extension educators.

• Korean Journal of Mathematics
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• v.23 no.3
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• pp.323-326
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• 2015

We prove that if a subfield of the Hilbert class field of an imaginary quadratic field k meets the anticyclotomic $\mathbb{Z}_p$-extension $k^a_{\infty}$ of k, then it is contained in $k^a_{\infty}$. And we give an example of an imaginay quadratic field k with ${\lambda}_3(k^a_{\infty}){\geq}8$.

• ETRI Journal
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• v.30 no.2
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• pp.326-334
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• 2008

This paper proposes a method for generating a basis translation matrix between isomorphic extension fields. To generate a basis translation matrix, we need the equality correspondence of a basis between the isomorphic extension fields. Consider an extension field $F_{p^m}$ where p is characteristic. As a brute force method, when $p^m$ is small, we can check the equality correspondence by using the minimal polynomial of a basis element; however, when $p^m$ is large, it becomes too difficult. The proposed methods are based on the fact that Type I and Type II optimal normal bases (ONBs) can be easily identified in each isomorphic extension field. The proposed methods efficiently use Type I and Type II ONBs and can generate a pair of basis translation matrices within 15 ms on Pentium 4 (3.6 GHz) when $mlog_2p$ = 160.

• ETRI Journal
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• v.30 no.6
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• pp.818-825
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• 2008

This paper proposes an exponentiation method with Frobenius mappings. The main target is an exponentiation in an extension field. This idea can be applied for scalar multiplication of a rational point of an elliptic curve defined over an extension field. The proposed method is closely related to so-called interleaving exponentiation. Unlike interleaving exponentiation methods, it can carry out several exponentiations of the same base at once. This happens in some pairing-based applications. The efficiency of using Frobenius mappings for exponentiation in an extension field was well demonstrated by Avanzi and Mihailescu. Their exponentiation method efficiently decreases the number of multiplications by inversely using many Frobenius mappings. Compared to their method, although the number of multiplications needed for the proposed method increases about 20%, the number of Frobenius mappings becomes small. The proposed method is efficient for cases in which Frobenius mapping cannot be carried out quickly.

• The Pure and Applied Mathematics
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• v.23 no.1
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• pp.53-59
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• 2016

Let G be a finite group containing a non-abelian Sylow 2-subgroup. We elementarily show that every G-Galois field extension L/K has a hyperbolic trace form in the presence of root of unity.

• Proceedings of the Korean Society of Crop Science Conference
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• 2006.04a
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• pp.634-635
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• 2006

• Communications of the Korean Mathematical Society
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• v.24 no.1
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• pp.1-4
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• 2009

In this paper we explicitly compute a Minkowski unit of a real abelian field and give a criterion when the first layer of anti-cyclotomic ${\mathbb{Z}}_3$-extension of an imaginary quadratic field is unramified everywhere.

• Korean Journal of Organic Agriculture
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• v.19 no.spc
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• pp.291-294
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• 2011

We studies a model for management of pepper anthracnose based covering method and spraying system in field. 1. Among 82 organic fungicides, 42 materials showed most effective inhibition against mycelia growth of the Colletotrichum acutatum in vitro. 23 formulated biocontrol agents were chosen to control the disease from 42 biocontrol agents in greenhouse. In the end, five kinds (2 plant extracts, 2 biopesiticides, 1 Bordeaux mixture) were selected from 23 materials in the field. 2. The mulching materials of bed covering in fruit season were thin non-woven fabric sheet and black plastic. The use of a fabric sheet was reduced the spread of anthracnose as compared to the plastic covering. 3. The application with the chosen materials was reduced 34% of anthracnose for 7 times sprays to planting 70 days as compared to the untreated control. In yield, nonwoven fabric sheet with formulated biopesticides was increased 17% than black plastic. 4. This result indicated that the developed biocontrol strategy could be an effective and economic crop protection system in organic pepper cultivation field.