Open Access Publications from the University of California

## Quantales and Hyperstructures

• Author(s): Dudzik, Andrew Joseph
We present a theory of lattice-enriched semirings, called \emph{quantic semirings}, which generalize both quantales and powersets of hyperrings. Using these structures, we show how to recover the spectrum of a Krasner hyperring (and in particular, a commutative ring with unity) via universal constructions, and generalize the spectrum to a new class of hyperstructures, \emph{hypersemirings}. (These include hyperstructures currently studied under the name semihyperrings'', but we have weakened the distributivity axioms.)