Abstract:

By introducing the concept of a left semicommutative nucleus  on a Quantale, we gave a characterization of the largest left semi-commutative quotient of a Quantale by means of its left presymmetric elements, proved that the category of left semicommutative Quantales are reflective subcategory of the category of Quantales, and discussed the relationships between localic nuclei and left semicommutative nuclei.

Key words: Quantale, quotient of Quantale, left semicommutative nucleus, localic nucleus