×

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.

MSC:

06F07 Quantales
PDF BibTeX XML Cite
Full Text: DOI

References:

[1] Dilworth R.P.: Noncommutative residuated lattices. Trans. Amer. Math. Soc. 46, 426–444 (1939) · Zbl 0022.10402
[2] Girard J.Y.: Linear Logic. Theoret. Comp. Sci. 50, 1–102 (1987) · Zbl 0625.03037
[3] Kruml D.: Spatial quantales. Appl. Categ. Structures 10, 49–62 (2002) · Zbl 0999.06015
[4] Mulvey C.J.: & . Suppl. Rend. Circ. Mat. PalermoSer.II 12, 99–104 (1986)
[5] Paseka, J.: Simple quantales. In: Proceedings of the Eighth Prague Topological Symposium(Toronto,1996), pp. 314–328(electronic). Topol. Atlas, North Bay(1997) · Zbl 0920.06007
[6] Paseka J., Kruml D.: Embeddings of quantales into simple quantales. J. Pure Appl. Algebra 148, 209–216 (2000) · Zbl 0962.06018
[7] Rosenthal K.I.: Quantales and Their Applications. Longman Scientific and Technical, New York (1990) · Zbl 0703.06007
[8] Yetter D.N.: Quantales and (noncommutative) linear logic. J. Symbolic Logic 55, 41–64 (1990) · Zbl 0701.03026
[9] Ward M.: Structure residuation. Ann. Math. 39, 558–569 (1938) · Zbl 0019.28902
[10] Ward M., Dilworth R.P.: Residuated lattice. Trans. Amer. Math. Soc. 45, 335–354 (1939) · Zbl 0021.10801
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.