Abstract
A lattice-ordered semiring R is a, complete-lattice-ordered semiring (CLO-semiring) if and only if (R, ∨, ∧) is a complete lattice. A CLO-semiring is a quantalic lattice-ordered semiring (QLO-semiring) if and only if multiplication distributes over arbitrary joins from either side; it is a frame-ordered semiring (FO-semiring) if and only if it is a QLO-semiring and the underlying complete lattice is a frame. As an immediate extension of Proposition 21.12(1), we see that if a a is an element of a CLO-semiring R then ∨(Ra) = a = ∨(aR).
Keywords
Nonempty Subset Maximal Element Complete Lattice Finite Subset Prime Element
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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Copyright information
© Springer Science+Business Media Dordrecht 1999