Characterizing weak fraction-dense and other coherent quantales by localization

In a recent work, Bhattacharjee and Dube [Algebra Universalis 83 (2022) #6] introduced the notion of fraction-dense frames as a generalization of fraction-dense f -rings, previously defined by Hager and Martinez [Canad.J. Math.45 (1993) 977-996].In this paper, the concept of fraction-dense frames is extended to the context of quantale theory.For this purpose, two notions are defined: weak fraction-dense quantales and fraction-dense quantales.(In the case of semiprime coherent quantales, these two notions coincide.)Weak fraction-dense coherent quantales are characterized, along with other classes of coherent quantales -such as complemented quantales and P P -quantales -by using localization theory.