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Ordered Rings and Fields [PDF]
Formalized Mathematics, 2017 Summary We introduce ordered rings and fields following Artin-Schreier’s approach using positive cones. We show that such orderings coincide with total order relations and give examples of ordered (and non ordered) rings and fields. In particular we show that polynomial rings can be ordered in (at least) two different ways [8, 5, 4, 9].
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Ordered intermetallic compounds combining precious metals and transition metals for electrocatalysis
Frontiers in Chemistry, 2022 Ordered intermetallic alloys with significantly improved activity and stability have attracted extensive attention as advanced electrocatalysts for reactions in polymer electrolyte membrane fuel cells (PEMFCs).
Meicheng Yang, Jinxin Wan, Chao Yan
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Journal of Pure and Applied Algebra, 1995 Let \(D\) be a division ring with involution *, center \(F\) and \([D : F] < \infty \). Since furthermore \(D\) is required to have a weak *-ordering, only the following two cases occur: (1) \((D,*)\) is a standard quaternion-algebra or (2) \([D : F]\) is odd.
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Proceedings of the American Mathematical Society, 1952 In this paper we shall give a necessary and sufficient condition that a skew field can be ordered; moreover, that the ordering of an ordered skew field K can be extended to an ordering of L, L being a given extension of K. The first of these two results generalizes to skew fields a theorem of E. Artin and 0.
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Ehrenfest relations and magnetoelastic effects in field-induced ordered phases
, 2005 Magnetoelastic properties in field-induced magnetic ordered phases are studied theoretically based on a Ginzburg-Landau theory. A critical field for the field-induced ordered phase is obtained as a function of temperature and pressure, which determine ...
Cavadini N. +28 more
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Exponentiation in power series fields
, 1996 We prove that for no nontrivial ordered abelian group G, the ordered power series field R((G)) admits an exponential, i.e. an isomorphism between its ordered additive group and its ordered multiplicative group of positive elements, but that there is a ...
Kuhlmann, Franz-Viktor +2 more
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Constructing Banaschewski compactification without Dedekind completeness axiom
International Journal of Mathematics and Mathematical Sciences, 2004 The main aim of this paper is to provide a construction of the Banaschewski compactification of a zero-dimensional Hausdorff topological space as a structure space of a ring of ordered field-valued continuous functions on the space, and thereby exhibit ...
S. K. Acharyya +2 more
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Proceedings of the Japan Academy, Series A, Mathematical Sciences, 1993 In Part I [ibid. 69, 45-48 (1993; Zbl 0795.11056)], the author gave a criterion for an arbitrary order to have class group generated by ambiguous ideals and also made a conjecture related to that criterion. Afterwards, however, counterexamples to the conjecture were found [cf. Part III, ibid. 70, 176-181 (1994; Zbl 0809.11064)].
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Effective impedance over ordered fields [PDF]
Journal of Mathematical Physics, 2021 In this paper, we study the properties of effective impedances of finite electrical networks, considering them as weighted graphs over an ordered field. We prove that a star-mesh transform of finite network does not change its effective impedance. Moreover, we consider two particular examples of infinite ladder networks (Feynman’s network or LC-network
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Hermitian Forms over Ordered ∗ -Fields
Journal of Algebra, 1999 Let \((D,{}^*)\) be a skew field with an involution *. Let \(Y_D\) and \(X_D\) denote space of Baer orderings and its subspace of *-orderings on \((D,{}^*).\) The main object of interest of the paper is the subring \(WS(D,{}^*)\) of the ring \({\mathcal C}(Y_D,Z)\) of continuous functions from \(Y_D\) to the ring of integers generated by the image of ...
Craven, Thomas C, Smith, Tara L
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