• 한국수학사학회지
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• 제19권4호
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• pp.97-106
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• 2006

격자의 기원은 수학에서 비롯된 것이 아니고 논리학에서 시작되었다([22]). 1880 년경 Peirce는 모든 격자는 분배 격자라고 생각하였으나 1890년경 $Schr{\"{o}}der$가 오류를 수정하였고, 1933년 Birkhoff가 lattice라는 단어를 처음 사용하였으나 이는 오늘의 격자와는 그 정의가 다르다. 이 논문에서는 Peirce를 소개하고 atomic 격자, atomistic 격자, J-격자, strong 격자 그리고 분배 격자의 상관관계를 연구한다.

• 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.

• 대한수학회논문집
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• 제13권4호
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• pp.751-757
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• 1998

Using idempotents in quasi-lattices, we show that the category Latt of lattices is both reflective and coreflective in the category qLatt of quasi-lattices and homomorphisms. It is also shown that a quasi-ordered set is a quasi-lattice iff its partially ordered reflection is a lattice.

• Journal of applied mathematics & informatics
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• 제38권1_2호
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• pp.79-89
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• 2020

We introduce the concepts of fuzzy join-complete lattices and Alexandrov L-pre-topologies in complete residuated lattices. We investigate the properties of fuzzy join-complete lattices on Alexandrov L-pre-topologies and fuzzy meet-complete lattices on Alexandrov L-pre-cotopologies. Moreover, we give their examples.

• Korean Journal of Mathematics
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• 제30권1호
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• pp.11-23
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• 2022

In this paper, the concept of pseudo - complementation on a generalized almost distributive fuzzy lattices (GADFLs) is introduced as a fuzzification of the crisp concept pseudo - complementation on a generalized almost distributive lattices. It is also established a one - to - one correspondence between the pseudo - complemented GADFL (R, A), R with 0 and the left identity element of R.

• 한국실내디자인학회논문집
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• 제23호
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• pp.139-147
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• 2000

The cultural identity of design is very critical in the modern society which is called the society of complex culture and multi-culture. In addition, adopting a traditional lattice-like pattern as a composition element of interior space is an effective way in the context of adding a traditional touch to the modern interior space. Meanwhile, in the process of applying Korean traditional lattices to modern interior space, some problems occurred: it has not been properly embodied; or it has been mistaken for those of China and Japan sharing similar culture with Korea. Thus, this study is designed to have precise knowledge of Korea, Chinese and Japanese traditional lattices. Besides, typical patterns of each nation's lattices are comparatively analyzed from the geometrical viewpoint, in a bid to pave the way for th modernization of traditional lattices. In particular, standards are set and proposed to identify different nations's lattices mainly focusing on grid type lattices which are often used and confusing.

• 대한수학회논문집
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• 제32권3호
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• pp.745-763
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• 2017

The Borel-Serre partial compactification gives cofinite models for the proper classifying space for arithmetic lattices. Non-arithmetic lattices arise only in semisimple Lie groups of ${\mathbb{R}}$-rank one. The author generalizes the Borel-Serre partial compactification to construct cofinite models for the proper classifying space for lattices in semisimple Lie groups of ${\mathbb{R}}$-rank one by using the reduction theory of Garland and Raghunathan.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제28권4호
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• pp.267-280
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• 2021

In this paper, we introduce the notions of fuzzy join (resp. meet) complete lattices and distance spaces in complete co-residuated lattices. Moreover, we investigate the relations between Alexandrov pretopologies (resp. precotopologies) and fuzzy join (resp. meet) complete lattices, respectively. We give their examples.

• 대한수학회논문집
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• 제11권1호
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• pp.33-41
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• 1996

In this article, all the universal totally positive integral ternary lattices over $Q(\sqrt{5})$ are determined.

• East Asian mathematical journal
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• 제28권3호
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• pp.333-337
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• 2012

Finiteness of regular normal binary Hermitian lattices are known in several articles. In this article, we point out that there are infinitely many imaginary quadratic fields that admit a regular subnormal binary Hermitian lattice.