Note on Representations of Ordered Semirings

Faigle, Ulrich and Peis, Britta (2006) Note on Representations of Ordered Semirings.
Technical Report , 14 p.
Submitted

Abstract

The article studies ordered semigroups and semirings with respect to their representations in lattices. Such structures are essentially the pseudolattices of Dietrich and Hoffman. It is shown that a subadditive representation implies the semigroup to be a lattice in its own right. In particular, distributive lattices can be characterized as semirings admitting subadditive supermodular representations. The cover problem asks for a minimal cover of a ground set by representing sets with respect to a semiring. A greedy algorithm is exhibited to solve the cover problem for the class of lattices with weakly subadditive and supermodular representation.


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Deposit Information:
ZAIK Number: zaik2006-521
Depositing User: Britta Peis
Date Deposited: 24 Mar 2006 00:00
Last Modified: 19 Dec 2011 09:44
URI: http://e-archive.informatik.uni-koeln.de/id/eprint/521