Totally ordered

English

Adjective

1. Template:Lb That is equipped with a total order, that is a subset of (the ground set of) a partially ordered set whose partial order is a total order with respect to said subset.

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   • 1976, K. D. Stroyan, W. A. J. Luxemburg, Introduction to the Theory of Infinitesimals, Template:W (Academic Press), page 67,

     (A.2.5) THEOREM If A is a totally ordered ring and if I is a proper order ideal, then A/I is a totally ordered ring (with the operations and order given above).

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   • 1996, Scientific Books staff (translators), Vasiliǐ M. Kopytov, Nikolaǐ Ya. Medvedev, Right-Ordered Groups, Scientific Books, page 98,

     We introduce the following notation:

     $G$ is a transitive group of order automorphisms of a totally ordered set $X$,

     $\theta$ is a convex $G$-congruence on the totally ordered set $X$,

     $\xi$ is the order type of the totally ordered set $X$,

     $\bar{\eta }$ is the order type of some class $Y=x\eta$ of the congruence $\eta$,

     $\zeta$ is the order type of the totally ordered quotient set $X/\theta$ of the totally ordered set $X$ by the congruence $\theta$.

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Translations

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