The Use of Ultraproducts in Commutative Algebra

• Main Author: Schoutens, Hans (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Berlin, Heidelberg : Springer Berlin Heidelberg, 2010.
• Series: Lecture Notes in Mathematics, 1999
• Subjects: Mathematics.; Algebraic geometry.; Commutative algebra.; Commutative rings.; Commutative Rings and Algebras.; Algebraic Geometry.

In spite of some recent applications of ultraproducts in algebra, they remain largely unknown to commutative algebraists, in part because they do not preserve basic properties such as Noetherianity. This work wants to make a strong case against these prejudices. More precisely, it studies ultraprodu...

Table of Contents:

• Ultraproducts and ?o?’ Theorem
• Flatness
• Uniform Bounds
• Tight Closure in Positive Characteristic
• Tight Closure in Characteristic Zero. Affine Case
• Tight Closure in Characteristic Zero. Local Case
• Cataproducts
• Protoproducts
• Asymptotic Homological Conjectures in Mixed Characteristic.