scholarly journals Corrigendum to “Finiteness theorems and algorithms for permutation invariant chains of Laurent lattice ideals” [J. Symb. Comput. 50 (March 2013) 314–334]

2016 ◽  
Vol 74 ◽  
pp. 650-652
Author(s):  
Christopher J. Hillar ◽  
Abraham Martín del Campo
Keyword(s):  
Lattice Ideals ◽  
Finiteness Theorems

scholarly journals Finiteness theorems and algorithms for permutation invariant chains of Laurent lattice ideals

2013 ◽  
Vol 50 ◽  
pp. 314-334 ◽  
Author(s):  
Christopher J. Hillar ◽  
Abraham Martín del Campo
Keyword(s):  
Lattice Ideals ◽  
Finiteness Theorems

scholarly journals Computing generating sets of lattice ideals and Markov bases of lattices

2009 ◽  
Vol 44 (10) ◽  
pp. 1463-1476 ◽  
Author(s):  
Raymond Hemmecke ◽  
Peter N. Malkin
Keyword(s):  
Markov Bases ◽  
Generating Sets ◽  
Lattice Ideals

scholarly journals Generic lattice ideals

1998 ◽  
Vol 11 (2) ◽  
pp. 363-373 ◽  
Author(s):  
Irena Peeva ◽  
Bernd Sturmfels
Keyword(s):  
Lattice Ideals

scholarly journals Finiteness theorems for algebraic cycles of small codimension on quadric fibrations over curves

2009 ◽  
Vol 7 (4) ◽  
Author(s):  
Cristian González-Avilés
Keyword(s):  
Algebraic Cycles ◽  
Finitely Generated ◽  
Relative Dimension ◽  
Finiteness Theorems ◽  
Small Codimension

AbstractWe obtain finiteness theorems for algebraic cycles of small codimension on quadric fibrations over curves over perfect fields. For example, if k is finitely generated over ℚ and X → C is a quadric fibration of odd relative dimension at least 11, then CH i(X) is finitely generated for i ≤ 4.

Hilbert on Theology and Its Discontents

2012 ◽  
Author(s):  
Colin McLarty
Keyword(s):  
Doctoral Student ◽  
Finiteness Theorems

This chapter examines the myth surrounding Paul Gordan's response to David Hilbert's finiteness theorems. A proof introduced by Hilbert in 1888 became the paradigm of modern axiomatic mathematics. In the myth, Gordan denounced Hilbert's proof, and his anathema rebounded against himself when he said, “This is not Mathematics, it is Theology!” After providing the background to the various interpretations that Gordan's comment has generated, the chapter considers the so-called “Gordan's problem”—to find finite complete systems of invariants for forms. It then discusses Hilbert's theorem and Gordan's reaction to Hilbert's fuller version of the invariant theorem, as well as Gordan's mythic quotation. It also explores the role played by Gordan's one and only doctoral student, Emmy Noether, in the Gordan–Hilbert controversy and concludes by emphasizing Gordan's story as an example of the deliberate use of narrative in mathematics.

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