About: Partially ordered ring

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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.

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  • 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 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. (en)
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  • Partially Ordered Ring (en)
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  • PartiallyOrderedRing (en)
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  • 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. (en)
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  • Partially ordered ring (en)
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