• 대한수학회논문집
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• 제10권2호
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• pp.285-292
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• 1995

Some nonpath-connected orthomodular lattices are given : Every infinite direct product of othomodular lattices containing infinitely many non-Boolean factors is a nonpath-connected orthomodular lattice. The orthomodular lattice of all closed subspaces of an infinite dimensional Hilbert space is a nonpath-connected orthomodular lattice.

• 대한수학회보
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• 제46권5호
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• pp.845-856
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• 2009

A block of an orthomodular lattice L is a maximal Boolean subalgebra of L. A site is a subalgebra of an orthomodular lattice L of the form S = A $\cap$ B, where A and B are distinct blocks of L. An orthomodular lattice L is called with finite sites if |A $\cap$ B| < $\infty$ for all distinct blocks A, B of L. We prove that there exists a weakly path-connected orthomodular lattice with finite sites which is not path-connected and if L is an orthomodular lattice such that the height of the join-semilattice [ComL]$\vee$ generated by the commutators of L is finite, then L is pathconnected.

• 대한수학회논문집
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• 제12권3호
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• pp.513-519
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• 1997

We show that each orthomodular lattice containing only atomic nonpath-connected blocks is a full subalgebra of an irreducible path-connected orthomodular lattice and there is a path-connected orthomodualr lattice L containing a weakly path-connected full subalgebra C(x) for some element x in L.

• 대한수학회논문집
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• 제19권2호
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• pp.197-204
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• 2004

Every orthomodular lattice satisfying the loop lemma is the direct product of a Boolean algebra and an irreducible path-connected orthomodular lattice.

• 대한수학회지
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• 제33권2호
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• pp.217-225
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• 1996

An orthomodular lattice (abbreviated by OML) is an ortholattice L which satisfies the orthomodular law: if x $\leq$ y, then $y = x \vee (x' \wedge y)$ [5]. A Boolean algebra B is an ortholattice satisfying the distributive law : $x \vee (g \wedge z) = (x \vee y) \wedge (x \vee z) \forall x, y, z \in B$.

• 대한수학회논문집
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• 제18권2호
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• pp.207-214
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• 2003

There exist two distinct Symmetric differences in a non Boolean orthomodular lattics. Let L be an orthomodular lattice. Then L is a Boolean algebra if and only if one symmetric difference is equal to the other. An orthomodular lattice L is Boolean if and only if one of two symmetric differences of L is associative.

• 대한수학회논문집
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• 제15권3호
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• pp.511-519
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• 2000

If G is a strict generalized orthomodular lattice and H={I｜I=[0, $\chi$, $\chi$$\in$G}, then H is prime ideal of the Janowitz's hull J(G) of G. If f is the janowitz's embedding, then the set of all commutatiors of f(G) equals the set of all commutators of the Janowitz's hull J(G) of G. Let L be an OML. Then L J(G) for a strict GOML G if and only if ther exists a proper nonprincipal prime ideal G in L.

• 한국콘텐츠학회:학술대회논문집
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• 한국콘텐츠학회 2013년도 춘계 종합학술대회 논문집
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• pp.369-370
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• 2013

Orthomodular lattice is a mathematical description of quantum theory which is based on the family CS(H) of all closed subspaces of a Hilbert space H. A partial multiplier is a function F from a non-empty subset D of a commutative semigroup A into A such that F(x)y = xF(y) for every elements x, y in A. In this paper, we define the notion of multipliers on orthomodular lattices and give some properties of multipliers. Also, we characterize some properties of orthomodular lattices by multipliers.

• 융합정보논문지
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• 제7권3호
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• pp.65-71
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• 2017

양자논리는 양자역학을 위한 수학적 구조인 힐버트 공간에서의 사영을 다루기 위해 Birkhoff와 von Neumann에 의해 소개되었고 Husimi는 이 양재논리를 보완하기 위해 직교모듈라의 성질과 직교모듈라 격자를 제안하였다. Abbott은 직교모듈라 격자에서의 함의를 연구하기 위해 직교함의 대수와 그 성질을 소개하였다. 직교모듈라 격자에서 가환관계는 분배법칙과 모듈라 성질 등과 관련된 중요한 성질이다. 본 논문에서는 직교함의 대수에서의 한 이항연산과 이를 이용한 최대하계를 정의하고 그 이항연산의 성질을 밝힌다. 또한 준동형사상을 정의하고 이를 이용하여 직교함의 대수에서의 가환관계를 특성화한다.

• 대한수학회보
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• 제31권1호
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• pp.61-72
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• 1994

Every irreducible block-finite orthomodular lattice is simple [9] and every irreducible orthomodular alttice such that no proper p-ideal of L contains infinitely many commutators is simple [5]. Every finite (height) OML L which does not belong to the varitety generated by MO2 has one of the OML MO3, 2$^{3}$.2$^{2}$, D$_{16}$ OMLHOUSE as the homomorpyhic image of a subalgebra of L [3]. In this paper, we extend these results.s.