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Algebraic and Categorical Aspects of Quantales
Publisher Summary This chapter introduces the basic notions in theory of quantales. It describes the aspects of algebraic and categorical properties of quantales and quantale modules. This chapterExpand
A direct proof of the Hofmann-Mislove theorem
The Hofmann-Mislove Theorem has attracted increasing interest. Through this note we intend to make it easily accessible by a simple direct proof
Hilbert Q-Modules and Nuclear Ideals in the Category of v-Semilattices with a Duality
Using this approach to V-semilattices with a duality i.e. Hilbert 2-modules, a nuclear traced ideal is described and nuclear maps in the respective category are characterized. Expand
Embeddings of quantales into simple quantales
Every quantale can be embedded into a simple quantale and every involutive quantale can be embedded into a somple involutive quantale. The image satisfies an analog of the von Neumann bicommutantExpand
Regular and normal quantales
Quantales can be viewed as a framework for a non—commutative topology. Basic properties of quantales are given. There are considered regular and normal quantales. The main, result asserts thatExpand
Filters on Some Classes of Quantum B-Algebras
In this paper, we continue the study of quantum B-algebras with emphasis on filters on integral quantum B-algebras. We then study filters in the setting of pseudo-hoops. First, we establish anExpand
The inheritance of BDE-property in sharply dominating lattice effect algebras and (o)-continuous states
For compactly generated Archimedean lattice effect algebras the equivalence of (o)-continuity of states with their complete additivity is proved and the “State smearing theorem” is proved. Expand
Interior tensor product of Hilbert modules
The interior tensor product in the context of the theory of Hilbert modules over involutive quantales is studied. Associativity, functoriality and representability via compact maps of the interiorExpand
On injective constructions of S-semigroups
The injectives in the category of S-semigroups with subhomomorphisms generalize the quantale algebras introduced by Solovyov, which provide a convenient universally algebraic framework for developing lattice-valued analogues of fuzzification. Expand