Geodesic
On maximal and minimal linear matching property
Algebra and discrete mathematics, Tome 15 (2013) no. 2, pp. 174-178.

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The matching basis in field extentions is introduced by S. Eliahou and C. Lecouvey in [2]. In this paper we define the minimal and maximal linear matching property for field extensions and prove that if $K$ is not algebraically closed, then $K$ has minimal linear matching property. In this paper we will prove that algebraic number fields have maximal linear matching property. We also give a shorter proof of a result established in [6] on the fundamental theorem of algebra.
Keywords: Linear matching property, Algebraic number field, Field extension, Maximal linear matching property, Minimal linear matching property. 
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M. Aliabadi; M. R. Darafsheh. On maximal and minimal linear matching property. Algebra and discrete mathematics, Tome 15 (2013) no. 2, pp. 174-178. http://geodesic.mathdoc.fr/item/ADM_2013_15_2_a3/

[1] S. Akbari, M. Aliabadi, Erratum to: Matching Subspaces in a field extension, submitted

[2] S. Eliahou, C. Lecouvey, “Mathching subspaces in a field extension”, J. Algebra, 324 (2010), 3420–3430 | DOI | MR | Zbl

[3] C. K. Fan, J. Losonczy, “Matchings and canonical forms in symmetric tensors”, Adv. Math., 117 (1996), 228–238 | DOI | MR | Zbl

[4] D. S. Malik, J. N. Mordeson, M. K. Sen, Fundamentals of Abstract Algebra, McGraw Hill, 1999

[5] H. Marksaitis, “Some remarks on subfields of algebraic number fields”, Lithuanian Mathematical Journal, 35:2 (1995) | DOI | MR | Zbl

[6] J. Shipman, “Improving of fundamental theorem of algebra”, Math. Intelligencer, 29:4 (2007), 9–14 | DOI | MR | Zbl

[7] E. K. Wakeford, “On canonical forms”, Proc. London Math. Soc., 18 (1918–1919), 403–410 | MR