Topics in Tight Closure Theory.

Tight Closure Theory;Phantom Homology;Test Elements;Mathematics;Science;Mathematics

Ananyan, Tigran SamveliTappenden, James P. ;

University of Michigan

关键词: Tight Closure Theory;    Phantom Homology;    Test Elements;    Mathematics;    Science;    Mathematics;   

Others  :  https://deepblue.lib.umich.edu/bitstream/handle/2027.42/63668/antigran_1.pdf?sequence=1&isAllowed=y

瑞士|英语

来源: The Illinois Digital Environment for Access to Learning and Scholarship

【 摘 要 】

The dissertation adresses some properties of the phantom projective resolutions. The main results are the counterexamples to 15 year old conjectures stated by I. Aberbach in [1]. In the thesis it is shown that a module can have a finite phantom projective dimension locally but not globally, and that a direct summand of amodule of finite phantom projective dimension can have itself have no finite phantom projective resolution. Along the way some technique dealing with reducing the phantom resolution to simpler forms is developed. Another important result is acharacterization of test elements for tight closure for some wide class of rings R interms of module-finite extensions of R within R^{1/p}.