Author | Greco, Silvio. author |
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Title | Topics in ฤ-adic Topologies [electronic resource] / by Silvio Greco, Paolo Salmon |
Imprint | Berlin, Heidelberg : Springer Berlin Heidelberg, 1971 |
Connect to | http://dx.doi.org/10.1007/978-3-642-88501-3 |
Descript | VII, 76 p. online resource |
Content -- ยง 1 Compatibilities of algebraic and topological structures on a set. The ?-adic topology. Artin-Rees lemma. Krullโs intersection theorem. Zariski rings -- ยง 2 Completions of filtered groups, rings and modules. Applications to ?-adic topologies -- ยง 3 Rings of formal and restricted power series. Preparation theorems. Hensel lemma -- ยง 4 Completions of finitely generated modules. Flatness and faithful flatness -- ยง 5 Noetherian properties of ?-adic completions -- ยง 6 Some general criteria of ascent and descent for ?-completions -- ยง7 Dimension of ?-completions -- ยง 8 Regularity and global dimension of ?-completions -- ยง 9 โCohen Macaulayโ and โGorensteinโ properties for ?-completions -- ยง 10 Integrity of ?-completions -- ยง 11 Unique factorization of ?-completions -- ยง 12 Fibers of a ring homomorphism and formal fibers of a ring -- ยง 13 Properties Sn and Rn for ?-completions -- ยง 14 Analytic reducedness -- ยง15 Normality of ?-completions -- References