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

Released on by Saul Lubkin
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  • Non-hausdorff Completion, A: The Abelian Category Of C-complete Left Modules Over A Topological Ring Book Detail

  • Author : Saul Lubkin
  • Release Date : 2015-05-28
  • Publisher : World Scientific Publishing Company
  • Genre : Mathematics
  • Pages : 352
  • ISBN 13 : 9814667404
  • File Size : 14,14 MB
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Non-hausdorff Completion, A: The Abelian Category Of C-complete Left Modules Over A Topological Ring by Saul Lubkin PDF Summary

Book Description: 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.

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