Orders and Order Closures for Not Necessarily Formally Real Fields
نویسندگان
چکیده
منابع مشابه
Counting Generalized Orders on Not Necessarily Formally Real Fields
The set of classical orderings of a field compatible with a given place from the field to the real numbers is known to be bijective with the set of homomorphisms from the value group of the place into the two element group. This fact is generalized here to the set of “generalized orders” compatible with an “extended absolute value,” i.e., an absolute value allowed to take the value ∞. The set o...
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(A) All rings in this announcement are commutative and with 1. For any ring K we denote by W(K) the Witt ring of nondegenerate symmetric bilinear forms over K. DEFINITION 1. A signature o of K is a ring homomorphism from W(K) to Z. REMARK 1. If K is a field, the signatures correspond uniquely with the orderings of K [3], [9]. Thus Theorem 1 below generalizes the main results of Artin-Schreier's...
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 1994
ISSN: 0021-8693
DOI: 10.1006/jabr.1994.1306