• 대한수학회보
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• 제53권4호
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• pp.971-983
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• 2016

A partially ordered set P is ideal-homogeneous provided that for any ideals I and J, if $$I{\sim_=}_{\sigma}J$$, then there exists an automorphism ${\sigma}^*$ such that ${\sigma}^*{\mid}_I={\sigma}$. Behrendt [1] characterizes the ideal-homogeneous partially ordered sets of height 1. In this paper, we characterize the ideal-homogeneous partially ordered sets of height 2 and nd some families of ideal-homogeneous partially ordered sets.

• Journal of applied mathematics & informatics
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• 제42권3호
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• pp.499-510
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• 2024

We introduce the concepts of right join-dense, right meet-dense, left join-dense and left meet-dense induced by bi-partially ordered sets on complete generalized residuated lattices. We investigate properties of these concepts and give an example related to them.

• 충청수학회지
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• 제25권1호
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• pp.105-113
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• 2012

Generalizing modular lattices, a concept of modular ordered sets was introduced by Chajda and Rachunek. In this paper, we characterize modular ordered sets as those partially ordered set P satisfying that for $a,\;b,\;c\;{\in}\;P\;with\;b\;{\leq}\;c,\;l(a,\;b)\;=\;l(a,\;c)\;and\;u(a,\;b)\;=\;u(a,\;c)$ imply $b\;=\;c$. Using this, we obtain a sufficient condition for them. We also discuss the modularity of the Dedekind-MacNeille completions of ordered sets.

• Kyungpook Mathematical Journal
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• 제64권1호
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• pp.161-169
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• 2024

A semi-well ordered set is a partially ordered set in which every non-empty subset of it contains a least element or a greatest element. It is defined as an extension of the concept of well ordered sets. An attempt is made to identify the properties of a semi-well ordered set equipped with the order topology.

• Kyungpook Mathematical Journal
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• 제16권1호
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• pp.7-20
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• 1976

• 대한수학회지
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• 제11권1호
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• pp.7-17
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• 1974

• 한국수학교육학회지시리즈A:수학교육
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• 제24권1호
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• pp.1-3
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• 1985

• Kyungpook Mathematical Journal
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• 제5권1호
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• pp.9-13
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• 1962

• 한국지능시스템학회논문지
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• 제17권7호
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• pp.981-985
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• 2007

In this paper, we investigate the properties of residuated partially ordered sets as weak definitions of algebraic structures in many valued logics. We study the left(resp. right) residuated semigroups induced by right(resp. left) associated map. We give their examples.

• Nonlinear Functional Analysis and Applications
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• 제28권2호
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• pp.571-587
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• 2023

In this paper, we have developed the idea of α-β-ψ-contractive mapping in S-metric space and renamed it α_s-β_s-ψ-contractive mapping. We have proved some results of fixed point present in literature in partially ordered S-metric space using α_s-β_s-admissible and α_s-β_s-ψ-contractive mapping.