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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Editorial actions: | ![]() |
Item Type: | Paper (Technical Report) |
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Citations: | 0 (Google Scholar) | |
Uncontrolled Keywords: | lattices covering problem subadditivity |
Subjects: |
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Divisions: | Institute of Computer Science > Computer Science Department - Prof. Dr. Schrader Mathematical Institute > Prof. Dr. Faigle |
Related URLs: |
ZAIK Number: | zaik2006-521 |
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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 |