• 한국데이타베이스학회:학술대회논문집
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• 한국데이타베이스학회 2000년도 추계학술대회 E-Business와 정보보안
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• pp.119-123
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• 2000

In this note, we study recent results concerning simplicity and spatiality of involutive quantales from the algebraic point of view. When S is a sup-lattice (with a duality), Q(S)$\times$Q( $S^{op}$ ) (Q(S)) is an involutive quantale. Using this, some characterizations of simplicity and spatiality of involutive quantales are investigated.

• International Journal of Fuzzy Logic and Intelligent Systems
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• 제7권3호
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• pp.193-197
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• 2007

We investigate the properties of fuzzy relations and meet preserving maps on strictly two-sided, commutative quantales. Moreover, we study the relations between them.

• 대한수학회지
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• 제56권5호
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• pp.1285-1307
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• 2019

For a multiplication R-module M we consider the Zariski topology in the set Spec (M) of prime submodules of M. We investigate the relationship between the algebraic properties of the submodules of M and the topological properties of some subspaces of Spec (M). We also consider some topological aspects of certain frames. We prove that if R is a commutative ring and M is a multiplication R-module, then the lattice Semp (M/N) of semiprime submodules of M/N is a spatial frame for every submodule N of M. When M is a quasi projective module, we obtain that the interval ${\uparrow}(N)^{Semp}(M)=\{P{\in}Semp(M){\mid}N{\subseteq}P\}$ and the lattice Semp (M/N) are isomorphic as frames. Finally, we obtain results about quantales and the classical Krull dimension of M.

• International Journal of Fuzzy Logic and Intelligent Systems
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• 제8권1호
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• pp.37-41
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• 2008

In this paper, we investigate the properties of implicative closure operators on the stsc-quantale L. We find implicative closure operators induced by a function.

• 한국지능시스템학회논문지
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• 제20권4호
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• pp.596-601
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• 2010

Weinvestigatethevariousoperationsoflowerandupperapproximationsonastscquantalelattice L.

• International Journal of Fuzzy Logic and Intelligent Systems
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• 제9권1호
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• pp.30-35
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• 2009

We investigate the properties of fuzzy relations, metrics and $\bigodot$-equivalence relation on a stsc quantale lattice L and a commutative cqm-lattice. In particular, pseudo-(quasi-) metrics induce $\bigodot$-(quasi)-equivalence relations.

• 한국지능시스템학회논문지
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• 제19권2호
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• pp.291-296
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• 2009

We investigate the properties of fuzzy relations and $\bigodot$-equivalence relation on a stsc quantale lattice L and a commutative cqm-lattice. In particular, we find $\bigodot$-equivalence relations induced by fuzzy relations.

• 한국지능시스템학회논문지
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• 제18권3호
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• pp.401-405
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• 2008

We investigate the properties of fuzzy relations and $\odot$-equivalence relation on a stsc quantale lattice L and a commutative cqm-lattice. In particular, fuzzy relations preserve(*, \otimes$)-equivalence relations where $\otimes$ are compositions, $\Rightarrow$ and $\Leftarrow$.