Non Hausdorff Completion A The Abelian Category Of C Complete Left Modules Over A Topological Ring
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Non-hausdorff Completion, A: The Abelian Category Of C-complete Left Modules Over A Topological Ring
Author: Saul Lubkin
language: en
Publisher: World Scientific Publishing Company
Release Date: 2015-05-28
This book introduces entirely new invariants never considered before, in homological algebra and commutative (and even non-commutative) algebra. The C-completion C(M), and higher C-completions, Cn(M), are defined for an arbitrary left module M over a topological ring A. Spectral sequences are defined that use these invariants. Given a left module over a topological ring A, under mild conditions the usual Hausdorff completion: M^ can be recovered from the C-completion C(M), by taking the quotient module by the closure of {0}.The new invariants and tools in this book are expected to be used in the study of p-adic cohomology in algebraic geometry; and also in the study of p-adic Banach spaces — by replacing the cumbersome 'complete tensor product' of p-adic Banach spaces, with the more sophisticated 'C-complete tensor product', discussed in this book.It is also not unlikely that the further study of these new invariants may well develop into a new branch of abstract mathematics - connected with commutative algebra, homological algebra, and algebraic topology.
Abelian Groups, Module Theory, and Topology
Features a stimulating selection of papers on abelian groups, commutative and noncommutative rings and their modules, and topological groups. Investigates currently popular topics such as Butler groups and almost completely decomposable groups.
Slenderness
Author: Radoslav Milan Dimitric
language: en
Publisher: Cambridge University Press
Release Date: 2019
A leading expert presents a unified concept of slenderness in Abelian categories, with numerous open problems and exercises.