• 대한수학회논문집
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• 제28권1호
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• pp.79-85
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• 2013

The structure of a poset P with smallest element 0 is looked at from two view points. Firstly, with respect to the Zariski topology, it is shown that Spec(P), the set of all prime semi-ideals of P, is a compact space and Max(P), the set of all maximal semi-ideals of P, is a compact $T_1$ subspace. Various other topological properties are derived. Secondly, we study the semi-ideal-based zero-divisor graph structure of poset P, denoted by $G_I$ (P), and characterize its diameter.

• Kyungpook Mathematical Journal
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• 제62권4호
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• pp.657-671
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• 2022

Where S is a pomonoid, let Pos-S be the category of S-posets and S-poset maps. We start off by characterizing the pomonoids S for which all projectives in this category are either generators or free. We then study the notions of regular injectivity and weakly regularly d-injectivity in this category. This leads to homological classification results for pomonoids. Among other things, we get find relationships between regular injectivity in the slice category Pos-S/BS, for any S-poset BS, and generators and cyclic projectives in Pos-S.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제7권1호
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• pp.19-26
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• 2000

The purpose of the paper is to show that in the Fraenkel-Mostowski topos, the category of the Boolean algebras has enough injectives.

• International Journal of Fuzzy Logic and Intelligent Systems
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• 제13권4호
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• pp.345-351
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• 2013

In this paper, we investigate the properties of fuzzy Galois (dual Galois, residuated, and dual residuated) connections in a complete residuated lattice L. We give their examples. In particular, we study fuzzy Galois (dual Galois, residuated, dual residuated) connections induced by L-fuzzy relations.

• International Journal of Fuzzy Logic and Intelligent Systems
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• 제11권2호
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• pp.129-134
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• 2011

We investigate the properties of Galois, dual Galois, residuated, and dual residuated connections on posets. In particular, we show that their connections are related to relations.

• 호남수학학술지
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• 제43권4호
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• pp.741-749
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• 2021

A variant of up-down posets described below and the number of their linear extensions were studied. We obtained the exponential generating functions which showed that how they are related to the Euler's up-down numbers.

• 호남수학학술지
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• 제38권1호
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• pp.71-84
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• 2016

The aim of this work is to compute the volume of the graph polytope associated with various type of finite simple graphs composed of paths and stars. Recurrence relations are obtained using the recursive volume formula (RVF) which was introduced in Lee and Ju ([3]). We also discussed the relationship between the volume of the graph polytopes and the number of linear extensions of the associated posets for given bipartite graphs.

• 대한수학회보
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• 제47권3호
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• pp.633-643
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• 2010

In this paper, the concept of maximal ideals relative to a filter on posets is introduced and examined. An intrinsic characterization of distributive lattices is obtained. In addition, we also give a characterization of pseudo primes in semicontinuous lattices and a characterization of semicontinuous lattices. Functions of semicontinuous lattices which are order preserving and semicontinuous are studied. A new concept of semiarithmetic lattices is introduced and examined.

• 대한수학회보
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• 제33권3호
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• pp.393-395
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• 1996

Let P be a finite poset and let $\mid$P$\mid$ be the number of vertices in pp. A Subposet of P is a subset of P with the induced order. A chain C in P is a subposet of P which is a linear order. The length of the chain C is $\mid$C$\mid$ - 1. A poset is bipartite if the length of each maximal chain is one.

• 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.