| 書目名稱 | Topics in m-adic Topologies | | 編輯 | Silvio Greco,Paolo Salmon | | 視頻video | http://file.papertrans.cn/927/926324/926324.mp4 | | 叢書名稱 | Ergebnisse der Mathematik und ihrer Grenzgebiete. 2. Folge | | 圖書封面 |  | | 描述 | 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 p | | 出版日期 | Book 1971 | | 關(guān)鍵詞 | Topologies; algebra; algebraic geometry; commutative algebra; homomorphism; m-adische Topologie; ring; topo | | 版次 | 1 | | doi | https://doi.org/10.1007/978-3-642-88501-3 | | isbn_softcover | 978-3-642-88503-7 | | isbn_ebook | 978-3-642-88501-3 | | copyright | Springer-Verlag Berlin · Heidelberg 1971 |
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