JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2015, Vol. 50 ›› Issue (02): 47-54.doi: 10.6040/j.issn.1671-9352.0.2014.207

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The projective objects in the category of fuzzy quantales

LU Jing, ZHAO Bin   

  1. School of Mathematics and Information Science, Shaanxi Normal University, Xi'an 710062, Shaanxi, China
  • Received:2014-05-08 Revised:2014-11-03 Online:2015-02-20 Published:2015-01-27

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Abstract: The concept of fuzzy weakly ⊗-stable completely distributive lattices is introduced. It is proved that the family of all down sets of a fuzzy ordered semigroup with a appropriate operation ⊗ is a fuzzy weakly ⊗-stable completely distributive lattice. A necessary and sufficient condition for a fuzzy completely distributive lattice to be a fuzzy weakly ⊗-stable completely distributive lattice is given. Finally, projective objects in the category of fuzzy quantales are studied. It is also proved that the E-projective objects in the category of fuzzy quantales are exactly the fuzzy weakly ⊗-stable completely distributive lattices.

Key words: -stable completely distributive lattice, fuzzy completely distributive lattice, projective object, fuzzy weakly ⊗

CLC Number: 

  • O153.1
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