2004•Journal of Shaanxi Normal UniversityRequires access

Characterization of idempotent left-side spatial Quantale

Bin Zhao

Abstract

Some basic properties of idempotent left-side Quantale are given. And it is obtained that a product of spatial Quantale and sub-Quantale of a spatial Quantale are spatial Quantale. By idempotent left-side simple Quantale being spatial Quantale, it is proved that an idempotent left-side Quantale is spatial iff it is a sub-Quantale of product of some idempotent left-side simple Quantale.

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Key concepts: Mathematics, Idempotence, Simple (philosophy), Pure mathematics, Product (mathematics), Algebra over a field, Geometry, Epistemology