The quantic conuclei on quantales. (English) Zbl 1183.06010

The main purpose of this paper is to investigate some properties of quantic conuclei. The concept of an ideal conucleus is introduced and a characterization for a map to be an ideal conucleus is given. Also the relations between quantic nuclei and quantic conuclei are studied on a Girard quantale, based on which the extensions of quantic conuclei (nuclei) to a Girard quantale and the relations between those extensions are discussed. Finally, it is proved that the number of subquantales of an infinite quantale is infinite.


06F07 Quantales
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