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CHARACTERIZATION OF PROJECTIVE QUANTALES

Part of: Boolean algebras (Boolean rings) Ordered structures Distributive lattices Lattices

Published online by Cambridge University Press:  08 January 2016

WOLFGANG RUMP
WOLFGANG RUMP*
Affiliation:
Institute for Algebra and Number Theory, University of Stuttgart, Pfaffenwaldring 57, D-70550 Stuttgart, Germany email rump@mathematik.uni-stuttgart.de
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Abstract

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It is proved that a quantale is projective if and only if it is isomorphic to a derived tensor quantale over a completely distributive sup-lattice. Furthermore, an intrinsic characterization of projectivity is given in terms of inertial sup-lattices and derivations of quantales.

Keywords

quantalesup-latticeinertial sup-latticelocalegraded quantalederived quantale

MSC classification

Primary: 06F07: Quantales
Secondary: 06D22: Frames, locales 06B23: Complete lattices, completions 06D15: Pseudocomplemented lattices
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 100 , Issue 3 , June 2016 , pp. 403 - 420
Copyright
© 2016 Australian Mathematical Publishing Association Inc. 

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