• Bulletin of the Korean Mathematical Society
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• v.50 no.2
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• pp.627-637
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• 2013

Let [$n$] = {1, 2, ${\ldots}$, $n$} be ordered in the standard way. The order-preserving full transformation semigroup ${\mathcal{O}}_n$ is the set of all order-preserving singular full transformations on [$n$] under composition. For this semigroup we describe maximal subsemibands, maximal regular subsemibands, locally maximal regular subsemibands, and completely obtain their classification.

• Bulletin of the Korean Mathematical Society
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• v.41 no.3
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• pp.465-472
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• 2004

A group G is said to satisfy the maximal condition on infinite normal subgroups if there does not exist an infinite properly ascending chain of infinite normal subgroups. We characterize the structure of locally nilpotent groups satisfying this chain condition. We then show how to construct locally nilpotent groups with the maximal condition on infinite normal subgroups, but not the maximal condition on subgroups.

• Journal of the Chungcheong Mathematical Society
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• v.30 no.2
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• pp.177-181
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• 2017

Let $f:M{\rightarrow}M$ be a diffeomorphism of a compact smooth manifold M. In this paper, we show that $C^1$ generically, if a chain transitive set ${\Lambda}$ is locally maximal then it admits a dominated splitting. Moreover, $C^1$ generically if a chain transitive set ${\Lambda}$ of f is locally maximal then it has zero entropy.

• Journal of the Korean Mathematical Society
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• v.58 no.5
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• pp.1059-1079
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• 2021

We show that given any chain transitive set of a C¹ generic diffeomorphism f, if a diffeomorphism f has the eventual shadowing property on the locally maximal chain transitive set, then it is hyperbolic. Moreover, given any chain transitive set of a C¹ generic vector field X, if a vector field X has the eventual shadowing property on the locally maximal chain transitive set, then the chain transitive set does not contain a singular point and it is hyperbolic. We apply our results to conservative systems (volume-preserving diffeomorphisms and divergence-free vector fields).

• Journal of the Korean Mathematical Society
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• v.39 no.3
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• pp.397-410
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• 2002

In this paper, some inequalities for vector-valued maximal functions over locally compact Vienkin groups are obtained.

• Journal of the Chungcheong Mathematical Society
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• v.8 no.1
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• pp.29-36
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• 1995

• Kyungpook Mathematical Journal
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• v.58 no.1
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• pp.1-8
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• 2018

We prove that if R is a commutative ring, then every maximal ideal of R is idempotent if and only if every locally noetherian (locally artinian) R-module is semisimple.

• Journal of the Chungcheong Mathematical Society
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• v.6 no.1
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• pp.59-64
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• 1993

In this note, we shall give a maximal element existence theorem for condensing multimaps in a locally convex Hausdorff topological vector space.

• Journal of the Korean Mathematical Society
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• v.32 no.2
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• pp.289-300
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• 1995

Every group G has a unique maximal normal locally nilpotent subgroup $\Phi(G)$, called the Hirsh-Plotkin radical of G [9]. If G is a group, we define the upper Hirsh-Plotkin series of G to be the ascending series $1 = R_0 \leq R_1 \leq \ldots$ in which $R_{\alpha+1}/R_\alpha = \{Phi(G/R_\alpha)$ for each ordinal $\alpha and R_\beta = \cup_{\alpha<\beta}R_\alpha$ for each limit ordinal $\beta$. If $R_r = G$ for some natural number r, then G is said to have locally nilpotent length r. $(LN)^r$ denotes the calss of groups of locally nilpotent length at most r.

• Bulletin of the Korean Mathematical Society
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• v.36 no.4
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• pp.737-746
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• 1999

For a locally compact Abelian group G, and a commutative Banach algebra B, let $L^1$(G, B) be the Banach algebra of all Bochner integrable functions. We show that if G is noncompact and B is a semiprime Banach algebras in which every minimal prime ideal is cnotained in a regular maximal ideal, then $L^1$(G, B) contains no nontrivial separating idal. As a consequence we deduce some automatic continuity results for $L^1$(G, B).