Non-hausdorff Completion, A: The Abelian Category Of C-complete Left Modules Over A Topological Ring
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€85.99
A01=Saul Lubkin
Abelian Categories
Author_Saul Lubkin
Category=PBF
Commutative Algebra
Completions
Eilenberg-Moore Axioms
eq_isMigrated=1
eq_isMigrated=2
eq_nobargain
Homological Algebra
Infinite Sums
Topological Modules
Product details
- ISBN 9789814667388
- Publication Date: 10 Jul 2015
- Publisher: World Scientific Publishing Co Pte Ltd
- Publication City/Country: SG
- Product Form: Hardback
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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.
