Titlebook: Topics in m-adic Topologies; Silvio Greco,Paolo Salmon Book 1971 Springer-Verlag Berlin · Heidelberg 1971 Topologies.algebra.algebraic geo

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ocks, and a narrow production and export base. The Cook Islands, Fiji, Samoa, Palau, and Vanuatu in particular depend heavily on tourism earnings as a major foreign exchange earner while countries such as Kiribati, Samoa, Tonga, and Tuvalu depend heavily on remittances and foreign aid to support the

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Book 1971f 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

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ehension 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 p978-3-642-88503-7978-3-642-88501-3

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utative 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, normalit

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Rings of formal and restricted power series. Preparation theorems. Hensel lemma,The (.,..., ..)-adic topology of . induces the (.,..., .)-topology on the polynomial ring .[.,..., .] which is a subring of .[[.,..., .]]; every series may be approximated by polynomials, so the ring .[.,..., ..] is dense in .[[.,..., .]]. Thus we have the following proposition.

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,Compatibilities of algebraic and topological structures on a set. The m-adic topology. Artin-Rees lemma. Krull’s intersection theorem. Zariski rings,ebraic and topological structures above are compatible in the following sense: the mappings . × . → . defined by (.) ? . + . and . → . defined by . ? -. are continuous (equivalently: the mapping . × . → . given by (.) ? . - . is continuous). Then we say that . is a . (with respect to the two structu