Non-hausdorff Completion, A: The Abelian Category Of C-complete Left Modules Over A Topological Ring

di Saul Lubkin (Autore)

World Scientific Publishing Co Pte Ltd, 2015

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.

• Autore: Saul Lubkin
• Editore: World Scientific Publishing Co Pte Ltd
• Anno: 2015
• Rilegatura: Hardback
• Pagine: 352 p.
• EAN: 9789814667388

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