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In the second part of the article we define absolute values and the square root function [5].<\/jats:p>","DOI":"10.1515\/forma-2017-0024","type":"journal-article","created":{"date-parts":[[2018,3,28]],"date-time":"2018-03-28T22:16:22Z","timestamp":1522275382000},"page":"249-259","source":"Crossref","is-referenced-by-count":1,"title":["Formally Real Fields"],"prefix":"10.1515","volume":"25","author":[{"given":"Christoph","family":"Schwarzweller","sequence":"first","affiliation":[{"name":"Institute of Informatics Faculty of Mathematics, Physics and Informatics University of Gdansk Wita Stwosza 57, 80-308 Gdansk , Poland"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"374","published-online":{"date-parts":[[2018,3,28]]},"reference":[{"key":"2021040914351760203_j_forma-2017-0024_ref_001_w2aab3b7ab1b6b1ab1ab1Aa","doi-asserted-by":"crossref","unstructured":"[1] Grzegorz Bancerek, Czes\u0142aw Bylinski, Adam Grabowski, Artur Korni\u0142owicz, Roman Matuszewski, Adam Naumowicz, Karol Pak, and Josef Urban. Mizar: State-of-the-art and beyond. In Manfred Kerber, Jacques Carette, Cezary Kaliszyk, Florian Rabe, and Volker Sorge, editors, Intelligent Computer Mathematics, volume 9150 of Lecture Notes in Computer Science, pages 261-279. Springer International Publishing, 2015. ISBN 978-3-319-20614-1. doi: 10.1007\/978-3-319-20615-8 17.10.1007\/978-3-319-20615-817","DOI":"10.1007\/978-3-319-20615-8"},{"key":"2021040914351760203_j_forma-2017-0024_ref_002_w2aab3b7ab1b6b1ab1ab2Aa","unstructured":"[2] Adam Grabowski, Artur Korni\u0142owicz, and Adam Naumowicz. Four decades of Mizar. Journal of Automated Reasoning, 55(3):191-198, 2015. doi: 10.1007\/s10817-015-9345-1.10.1007\/s10817-015-9345-1"},{"key":"2021040914351760203_j_forma-2017-0024_ref_003_w2aab3b7ab1b6b1ab1ab3Aa","doi-asserted-by":"crossref","unstructured":"[3] Adam Grabowski, Artur Korni\u0142owicz, and Christoph Schwarzweller. On algebraic hierarchies in mathematical repository of Mizar. In M. Ganzha, L. Maciaszek, and M. Paprzycki, editors, Proceedings of the 2016 Federated Conference on Computer Science and Infor mation Systems (FedCSIS), volume 8 of Annals of Computer Science and Information Systems, pages 363-371, 2016. doi: 10.15439\/2016F520.","DOI":"10.15439\/2016F520"},{"key":"2021040914351760203_j_forma-2017-0024_ref_004_w2aab3b7ab1b6b1ab1ab4Aa","unstructured":"[4] Nathan Jacobson. Lecture Notes in Abstract Algebra, III. Theory of Fields and Galois Theory. Springer-Verlag, 1964."},{"key":"2021040914351760203_j_forma-2017-0024_ref_005_w2aab3b7ab1b6b1ab1ab5Aa","doi-asserted-by":"crossref","unstructured":"[5] Manfred Knebusch and Claus Scheiderer. Einf\u00a8uhrung in die reelle Algebra. Vieweg-Verlag, 1989.","DOI":"10.1007\/978-3-322-85033-1"},{"key":"2021040914351760203_j_forma-2017-0024_ref_006_w2aab3b7ab1b6b1ab1ab6Aa","doi-asserted-by":"crossref","unstructured":"[6] Alexander Prestel. Lectures on Formally Real Fields. Springer-Verlag, 1984.","DOI":"10.1007\/BFb0101548"},{"key":"2021040914351760203_j_forma-2017-0024_ref_007_w2aab3b7ab1b6b1ab1ab7Aa","unstructured":"[7] Knut Radbruch. Geordnete K\u00a8orper. Lecture Notes, University of Kaiserslautern, Germany, 1991."},{"key":"2021040914351760203_j_forma-2017-0024_ref_008_w2aab3b7ab1b6b1ab1ab8Aa","unstructured":"[8] Christoph Schwarzweller. The binomial theorem for algebraic structures. Formalized Mathematics, 9(3):559-564, 2001."},{"key":"2021040914351760203_j_forma-2017-0024_ref_009_w2aab3b7ab1b6b1ab1ab9Aa","unstructured":"[9] Christoph Schwarzweller. Ordered rings and fields. Formalized Mathematics, 25(1):63-72, 2017. doi: 10.1515\/forma-2017-0006.10.1515\/forma-2017-0006"},{"key":"2021040914351760203_j_forma-2017-0024_ref_010_w2aab3b7ab1b6b1ab1ac10Aa","doi-asserted-by":"crossref","unstructured":"[10] Christoph Schwarzweller. On roots of polynomials and algebraically closed fields. 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