Quantale

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In mathematics, quantales are certain partially ordered algebraic structures which generalize frames (pointless topologies) as well as various lattices of multiplicative ideals from ring theory and functional analysis (C*-algebras, von Neumann algebras).

A quantale is a complete lattice Q with an associative binary multiplication satisfying

x * sup { x_i | i in I } = sup { x * x_i | i in I }

sup { x_i | i in I } * x = sup { x_i * x | i in I }

for all x, x_i in Q, i in I (here I is any index set).

External link

Some Results on Simple Quantales by Jan Paseka