On invariants and strict systems of irreducible polynomials over Henselian valued fields

Khanduja, Sudesh K. ; Khassa, Ramneek (2011) On invariants and strict systems of irreducible polynomials over Henselian valued fields Communications in Algebra, 39 (2). pp. 584-593. ISSN 0092-7872

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Official URL: http://www.tandfonline.com/doi/abs/10.1080/0092787...

Related URL: http://dx.doi.org/10.1080/00927871003591934

Abstract

Let g(x) be a monic irreducible defectless polynomial over a henselian valued field (K, v), i.e., K(θ) is a defectless extension of (K, v) for any root θ of g(x). It is known that a complete distinguished chain for θ with respect to (K, v) gives rise to several invariants associated with g(x). Recently Ron Brown studied certain invariants of defectless polynomials by introducing strict systems of polynomial extensions. In this article, the authors establish a one-to-one correspondence between strict systems of polynomial extensions and conjugacy classes of complete distinguished chains. This correspondence leads to a simple interpretation of various results proved for strict systems. The authors give new characterizations of an invariant γ g introduced by Brown.

Item Type:Article
Source:Copyright of this article belongs to Taylor and Francis Group.
Keywords:Field Theory and Polynomials; Non-Archimedean Valued Fields; Valued Fields
ID Code:69902
Deposited On:19 Nov 2011 11:17
Last Modified:19 Nov 2011 11:17

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