Partially-Ordered Semirings

Jonathan S. Golan
Additional contact information
Jonathan S. Golan: University of Haifa

Chapter 20 in Semirings and their Applications, 1999, pp 223-237 from Springer

Abstract: Abstract Many of the semirings originally studied, such as ℕ and ideal(R), have a partial-order structure in addition to their algebraic structure and, indeed, the most interesting theorems concerning them make use of the interplay between these two structures. In is therefore natural for us to study semirings, and semimodules over them, on which a partial order is defined. A hemiring (R, +, •) is partially-ordered if and only if there exists a partial order relation ≤ on R satisfying the following conditions for elements r, r′, and r″ of R: (1) If r ≤ r′ then r + r″ ≤ r′ + r″; (2) If r ≤ r′ and r″ ≥ 0 then rr″ ≤ r′r″ and r″r ≤ r″r′.

Keywords: Partial Order; Riesz Space; Usual Order; Partial Order Relation; Infinite Element (search for similar items in EconPapers)
Date: 1999
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-94-015-9333-5_20

Ordering information: This item can be ordered from
http://www.springer.com/9789401593335

DOI: 10.1007/978-94-015-9333-5_20

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().