Show/Hide Menu
Hide/Show Apps
Logout
Türkçe
Türkçe
Search
Search
Login
Login
OpenMETU
OpenMETU
About
About
Open Science Policy
Open Science Policy
Communities & Collections
Communities & Collections
Help
Help
Frequently Asked Questions
Frequently Asked Questions
Guides
Guides
Thesis submission
Thesis submission
MS without thesis term project submission
MS without thesis term project submission
Publication submission with DOI
Publication submission with DOI
Publication submission
Publication submission
Supporting Information
Supporting Information
General Information
General Information
Copyright, Embargo and License
Copyright, Embargo and License
Contact us
Contact us
A geometric approach to absolute irreducibility of polynomials
Download
index.pdf
Date
2004
Author
Koyuncu, Fatih
Metadata
Show full item record
Item Usage Stats
186
views
63
downloads
Cite This
This thesis is a contribution to determine the absolute irreducibility of polynomials via their Newton polytopes. For any field F; a polynomial f in F[x1, x2,..., xk] can be associated with a polytope, called its Newton polytope. If the polynomial f has integrally indecomposable Newton polytope, in the sense of Minkowski sum, then it is absolutely irreducible over F; i.e. irreducible over every algebraic extension of F. We present some new results giving integrally indecomposable classes of polytopes. Consequently, we have some new criteria giving infinitely many types of absolutely irreducible polynomials over arbitrary fields.
Subject Keywords
Algebra.
URI
http://etd.lib.metu.edu.tr/upload/3/12604873/index.pdf
https://hdl.handle.net/11511/14096
Collections
Graduate School of Natural and Applied Sciences, Thesis
Suggestions
OpenMETU
Core
On the deformation chirality of real cubic fourfolds
Finashin, Sergey (Wiley, 2009-09-01)
According to our previous results, the conjugacy class of the involution induced by the complex conjugation in the homology of a real non-singular cubic fourfold determines the fourfold tip to projective equivalence and deformation. Here, we show how to eliminate the projective equivalence and obtain a pure deformation classification, that is, how to respond to the chirality problem: which cubics are not deformation equivalent to their image under a mirror reflection. We provide an arithmetical criterion of...
A generic identification theorem for L*-groups of finite Morley rank
Berkman, Ayse; Borovik, Alexandre V.; Burdges, Jeffrey; Cherfin, Gregory (Elsevier BV, 2008-01-01)
This paper provides a method for identifying "sufficiently rich" simple groups of finite Morley rank with simple algebraic groups over algebraically closed fields. Special attention is given to the even type case, and the paper contains a number of structural results about simple groups of finite Morley rank and even type.
Kummer extensions of function fields with many rational places
Gülmez Temur, Burcu; Özbudak, Ferruh; Department of Mathematics (2005)
In this thesis, we give two simple and effective methods for constructing Kummer extensions of algebraic function fields over finite fields with many rational places. Some explicit examples are obtained after a practical search. We also study fibre products of Kummer extensions over a finite field and determine the exact number of rational places. We obtain explicit examples with many rational places by a practical search. We have a record (i.e the lower bound is improved) and a new entry for the table of v...
An identification theorem for groups of finite Morley rank and even type
Berkman, A; Borovik, AV (Elsevier BV, 2003-08-15)
The paper contains a construction of a definable BN-pair in a simple group of finite Morley rank and even type with a sufficiently good system of 2-local parabolic subgroups. This provides 'the final identification theorem' for simple groups of finite Morley rank and even type.
The classical involution theorem for groups of finite Morley rank
Berkman, A (Elsevier BV, 2001-09-15)
This paper gives a partial answer to the Cherlin-Zil'ber Conjecture, which states that every infinite simple group of finite Morley rank is isomorphic to an algebraic group over an algebraically closed field. The classification of the generic case of tame groups of odd type follows from the main result of this work, which is an analogue of Aschbacher's Classical Involution Theorem for finite simple groups. (C) 2001 Academic Press.
Citation Formats
IEEE
ACM
APA
CHICAGO
MLA
BibTeX
F. Koyuncu, “A geometric approach to absolute irreducibility of polynomials,” Ph.D. - Doctoral Program, Middle East Technical University, 2004.