Partially Ordered Ring

(Ring Theory)

Tech

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Ring Theory
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What is Partially ordered ring?

In abstract algebra, a partially ordered ring is a ring (A, +, · ), together with a compatible partial order, i.e. a partial order on the underlying set A that is compatible with the ring operations in the sense that it satisfies: implies and and imply that for 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 ordered ring, also called a totally ordered ring, is a partially ordered ring where is additionally a total order. An l-ring, or lattice-ordered ring, is a partially ordered ring where is additionally a lattice order.

Technology Types

ordered algebraic structurering theory

Synonyms

F-ringLattice-ordered ringPierce-Birkhoff ringPierce–Birkhoff ringTotally-ordered ring

Tech Info


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