scholarly journals On Bézout inequalities for non-homogeneous polynomial ideals

2021 ◽  
Vol 106 ◽  
pp. 1-22
Author(s):  
Amir Hashemi ◽  
Joos Heintz ◽  
Luis M. Pardo ◽  
Pablo Solernó
Keyword(s):  
Homogeneous Polynomial ◽  
Polynomial Ideals

scholarly journals THE INVARIANTS FIELD OF SOME FINITE PROJECTIVE LINEAR GROUP ACTIONS

2011 ◽  
Vol 85 (1) ◽  
pp. 19-25
Author(s):  
YIN CHEN
Keyword(s):  
Finite Field ◽  
Projective Space ◽  
Vector Space ◽  
Orthogonal Group ◽  
Homogeneous Polynomial ◽  
Classical Group ◽  
Projective Group ◽  
Dimensional Vector ◽  
Dimensional Vector Space ◽  
Projective Linear Group

AbstractLet Fq be a finite field with q elements, V an n-dimensional vector space over Fq and 𝒱 the projective space associated to V. Let G≤GLn(Fq) be a classical group and PG be the corresponding projective group. In this note we prove that if Fq (V )G is purely transcendental over Fq with homogeneous polynomial generators, then Fq (𝒱)PG is also purely transcendental over Fq. We compute explicitly the generators of Fq (𝒱)PG when G is the symplectic, unitary or orthogonal group.

scholarly journals A uniqueness result on the decompositions of a bi-homogeneous polynomial

2016 ◽  
Vol 65 (4) ◽  
pp. 677-698 ◽  
Author(s):  
Edoardo Ballico ◽  
Alessandra Bernardi
Keyword(s):  
Homogeneous Polynomial ◽  
Uniqueness Result
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