On Brown's constant associated with irreducible polynomials over Henselian valued fields

Khanduja, Sudesh K. (2010) On Brown's constant associated with irreducible polynomials over Henselian valued fields Journal of Pure and Applied Algebra, 214 (12). pp. 2294-2300. ISSN 0022-4049

Full text not available from this repository.

Official URL: http://www.sciencedirect.com/science/article/pii/S...

Related URL: http://dx.doi.org/10.1016/j.jpaa.2010.02.028

Abstract

Let v be a henselian valuation of arbitrary rank of a field K and ν̅ be the prolongation of v to the algebraic closure K~ of K with value group G~.In 2008, Ron Brown gave a class P of monic irreducible polynomials over K such that to each g(x)there corresponds a smallest constant λg belonging to G~(referred to as Brown’s constant) with the property that whenever ν̅(g(β))is more than λg with K(β) a tamely ramified extension of (K,v), then K(β) contains a root of g(x). In this paper, we determine explicitly this constant besides giving an important property of λg without assuming that K(β)/K is tamely ramified.

Item Type:Article
Source:Copyright of this article belongs to Elsevier Science.
ID Code:69939
Deposited On:19 Nov 2011 11:16
Last Modified:19 Nov 2011 11:16

Repository Staff Only: item control page