S. Vijayabalaji, J. Parthiban
Department of Mathematics
University College of Engineering
(A Constituent College of Anna University, Chennai)
Pantruti, 607 106. Tamilnadu, INDIA
Department of Mathematics
Kurinji College of Engineering and Technology
Tiruchirappalli Dist, 621 307, Tamilnadu, INDIA

Abstract. Algebraic Number theory involves using techniques from Algebra and finite group theory to gain deeper understanding of number fields. Motivated by the theory of valued n-inner product over a valued field that was introduced by us; the main objective of this paper is to derive some interesting inequalities on valued n-inner product space combined with the theory of equations. We conclude with the definition of global field and prove that it plays major role in Algebraic Number theory.

Received: May 9, 2013

AMS Subject Classification: 26D15, 39B62

Key Words and Phrases: valued inner product, arithmetic mean of vectors

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