Abstract
We introduce and study mu-elements of integral commutative quantales, that generalize a lattice-theoretic abstraction (namely, essential elements) of essential ideals of rings, essential submodules of modules, and dense subsets of topological spaces. Exploring several examples, we show that mu-elements are indeed a genuine extension of essential elements. We study preservation of mu-elements under contractions and extensions of quantale homomorphisms. We introduce mu-complements and mu-closedness and study their properties. We determine mu-elements for several distinguished quantales, including ideals of Zn and open subsets of topological spaces. Finally, we provide a complete characterization of mu-elements in modular quantales.