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About: Partially ordered ring     Goto   Sponge   NotDistinct   Permalink

An Entity of Type : yago:Whole100003553, within Data Space : dbpedia.demo.openlinksw.com associated with source document(s)

Type: yago:WikicatOrderedAlgebraicStructuresyago:Artifact100021939yago:Object100002684yago:PhysicalEntity100001930yago:YagoGeoEntityyago:YagoPermanentlyLocatedEntityyago:Structure104341686yago:Whole100003553 New Facet based on Instances of this Class

In abstract algebra, a partially ordered ring is a ring (A, +, ·), together with a compatible partial order, that is, a partial order on the underlying set A that is compatible with the ring operations in the sense that it satisfies: andfor all . Various extensions of this definition exist that constrain the ring, the partial order, or both. For example, an Archimedean partially ordered ring is a partially ordered ring where 's partially ordered additive group is Archimedean. An l-ring, or lattice-ordered ring, is a partially ordered ring where is additionally a lattice order.