• Bulletin of the Korean Mathematical Society
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• v.59 no.3
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• pp.567-608
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• 2022

We show that certain extensions of classifiable C^*-algebras are strongly classified by the associated six-term exact sequence in K-theory together with the positive cone of K₀-groups of the ideal and quotient. We use our results to completely classify all unital graph C^*-algebras with exactly one non-trivial ideal.

• Bulletin of the Korean Mathematical Society
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• v.30 no.2
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• pp.285-293
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• 1993

In [4], Baumslag and Tretkoff proved a residual finiteness criterion for HNN extensions (Theorem 1.2, below). This result has been used extensively in the study of the residual finiteness of HNN extensions. Note that every one-relator group can be embedded in a one-relator group whose relator has zero exponent sum on a generator, and the latter group can be considered as an HNN extension. Hence the properties of an HNN extension play an important role in the study of one-relator groups [3], [2]. In this paper we prove a criterion for HNN extensions to be .pi.$_{c}$(Theorem 2.2). Moreover, we can prove that certain one-relator groups, known to be residually finite, are actually .pi.$_{c}$. It was known by Mostowski [10] that the word problem is solvable for finitely presented, residually finite groups. In the same way, the power problem is solvable for finitely presented .pi.$_{c}$ groups. Another application of subgroup separability with respect to special subgroups was mentioned by Thurston [12, Problem 15].m 15].

• Communications of the Korean Mathematical Society
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• v.33 no.2
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• pp.397-408
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• 2018

It is well-known that quasi-$Pr{\ddot{u}}fer$ domains are characterized as those domains D, such that every extension of D inside its quotient field is a primitive extension and that primitive extensions are characterized in terms of INC-extensions. Let $R={\bigoplus}_{{\alpha}{{\in}}{\Gamma}}$ $R_{\alpha}$ be a graded integral domain graded by an arbitrary torsionless grading monoid ${\Gamma}$ and ${\star}$ be a semistar operation on R. The main purpose of this paper is to give new characterizations of gr-${\star}$-quasi-$Pr{\ddot{u}}fer$ domains in terms of graded primitive and INC-extensions. Applications include new characterizations of UMt-domains.

• Communications of the Korean Mathematical Society
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• v.37 no.1
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• pp.65-74
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• 2022

A valued field (K, ν) is called defectless if each of its finite extensions is defectless. In [1], Aghigh and Khanduja posed a question on defectless extensions of henselian valued fields: "if every simple algebraic extension of a henselian valued field (K, ν) is defectless, then is it true that (K, ν) is defectless?" They gave an example to show that the answer is "no" in general. This paper explores when the answer to the mentioned question is affirmative. More precisely, for a henselian valued field (K, ν) such that each of its simple algebraic extensions is defectless, we investigate additional conditions under which (K, ν) is defectless.

• Bulletin of the Korean Mathematical Society
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• v.61 no.3
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• pp.785-796
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• 2024

Let p be a prime. A group G is said to be residually p-finite if for each non-trivial element x of G, there exists a normal subgroup N of index a power of p in G such that x is not in N. In this note we shall prove that certain HNN extensions of free abelian groups of finite rank are residually p-finite. In addition some of these HNN extensions are subgroup separable. Characterisations for certain one-relator groups and similar groups including the Baumslag-Solitar groups to be residually p-finite are proved.

• Journal of the Chungcheong Mathematical Society
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• v.10 no.1
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• pp.1-7
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• 1997

We characterize fuzzy ideals in near-rings and extensions of such ideals with the sup property.

• Journal of the Chungcheong Mathematical Society
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• v.20 no.4
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• pp.525-533
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• 2007

In this paper, we prove the continuity of the Zadeh extensions for continuous surjections and for semiflows.

• Journal of the Korean Mathematical Society
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• v.34 no.3
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• pp.599-608
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• 1997

In this paper we give a generalization of the well-known Borsuk-Ulam theorem and its extensions to countably many products of spheres.

• Journal of the Chungcheong Mathematical Society
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• v.15 no.2
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• pp.35-39
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• 2003

In this paper we study a ring over which every left module of finite length has an injective hull of finite length. We consider a ring that is a finite intermediate normalizing extension ring of such a ring. We also consider the subrings of such a ring.

• Honam Mathematical Journal
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• v.32 no.4
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• pp.791-795
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• 2010

We study the consequences of Gross's conjecture for cyclic extensions of degree $l^2$ where l is prime, and deduce that the L-values at s = 0 satisfy certain congruence relations.