A Non-Hausdorff Completion : The Abelian Category of C-complete Left Modules Over a Topological Ring

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 DEGREES 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.

Author: Saul Lubkin

Publisher: World Scientific Publishing Company

Publication Date: Jul 10, 2015

Number of Pages: 335 pages

Language: English

Binding: Hardcover

ISBN-10: 9814667382

ISBN-13: 9789814667388