Topics in M-adic Topologies - Ergebnisse Der Mathematik Und Ihrer Grenzgebiete. 2. Folge - Silvio Greco - Books - Springer-Verlag Berlin and Heidelberg Gm - 9783642885037 - April 10, 2012
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Silvio Greco
Topics in M-adic Topologies - Ergebnisse Der Mathematik Und Ihrer Grenzgebiete. 2. Folge Softcover Reprint of the Original 1st Ed. 1971 edition

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The m-adic topologies and, in particular the notions of m-complete ring and m-completion A of a commutative ring A, occur frequently in commutative algebra and are also a useful tool in algebraic geometry. The aim of this work is to collect together some criteria concerning the ascent (from A to A) and the descent (from A to A) of several properties of commutative rings such as, for example: integrity, regularity, factoriality, normality, etc. More precisely, we want to show that many of the above criteria, although not trivial at all, are elementary consequences of some fundamental notions of commutative algebra and local algebra. Sometimes we are able to get only partial results, which probably can be improved by further deeper investigations. No new result has been included in this work. Its only origi­ nality is the choice of material and the mode of presentation. The comprehension of the most important statements included in this book needs only a very elementary background in algebra, ideal theory and general topology. In order to emphasize the elementary character of our treatment, we have recalled several well known definitions and, sometimes, even the proofs of the first properties which follow directly from them. On the other hand, we did not insert in this work some important results, such as the Cohen structure theorem on complete noetherian local rings, as we did not want to get away too much from the spirit of the book.

83 pages, biography

Media Books     Paperback Book   (Book with soft cover and glued back)
Released April 10, 2012
ISBN13 9783642885037
Publishers Springer-Verlag Berlin and Heidelberg Gm
Pages 76
Dimensions 155 × 235 × 5 mm   ·   136 g
Language English  

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