A lattice-ordered skew-field is totally ordered if squares are positive

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dc.creatorYang, Yichuan
dc.date2005-05-18
dc.date2007-02-06
dc.date.accessioned2026-07-07T07:44:44Z
dc.date.available2026-07-07T07:44:44Z
dc.descriptionWe show that a lattice-ordered field (not necessarily commutative) is totally ordered if and only if each square is positive, answering a generalized question of Conrad and Dauns (Pacific J. Math. 30 (1969), 385--398) in the affirmative. As a consequence, any lattice-ordered skew field in (Brumfiel, Partially ordered rings and semi-algebraic geometry. Cambridge University Press, 1979) is totally ordered. Furthermore, we note that every lattice order determined by a {\it pre-positive cone} $P$ on a skew-filed $F$ is linearly ordered since $F^2\subseteq P$ (see P restel, Lectures on formally real fields, Lecture Notes in mathematics, 1093, Springer-Verlag, 1984).
dc.descriptionThe main part of the note was published in AMM
dc.identifierhttps://arxiv.org/abs/math/0505365
dc.identifierhttp://arxiv.org/abs/math/0505365
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/123307
dc.subjectRings and Algebras
dc.subjectAlgebraic Geometry
dc.subject06A70, 12J15
dc.titleA lattice-ordered skew-field is totally ordered if squares are positive
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