# Integral domains inside Noetherian power series rings : constructions and examples / William Heinzer, Christel Rotthaus, Sylvia Wiegand.

##### By: Heinzer, William J [author.].

##### Contributor(s): Rotthaus, Christel [author.] | Wiegand, Sylvia [author.].

Material type: TextSeries: Mathematical surveys and monographs, Volume 259.Publisher: Providence, Rhode Island : American Mathematical Society, [2021]Description: xi, 426 pages : USD 125.00 illustrations (black and white) ; 26 cm.Content type: text Media type: unmediated Carrier type: volumeISBN: 9781470466428.Subject(s): Noetherian rings | Integral domains | Commutative algebra -- General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to commutative algebra | Commutative algebra -- Instructional exposition (textbooks, tutorial papers, etc.) pertaining to commutative algebra | Commutative algebra -- Research exposition (monographs, survey articles) pertaining to commutative algebra | Commutative algebra -- General commutative ring theory -- Divisibility and factorizations in commutative rings | Commutative algebra -- Commutative ring extensions and related topics -- Integral dependence in commutative rings; going up, going down | Commutative algebra -- Commutative ring extensions and related topics -- Integral closure of commutative rings and ideals; integrally closed rings, related rings (Japanese, etc.) | Commutative algebra -- Commutative ring extensions and related topics -- Polynomials over commutative rings | Commutative algebra -- Commutative ring extensions and related topics -- Rings of fractions and localization for commutative rings | Commutative algebra -- Commutative ring extensions and related topics -- Completion of commutative rings | Commutative algebra -- Commutative ring extensions and related topics -- Étale and flat extensions; Henselization; Artin approximationDDC classification: 512.44 Other classification: 13-00 | 13-01 | 13-02 | 13A05 | 13B21 | 13B22 | 13B25 | 13B30 | 13B35 | 13B40 Also issued online.Item type | Current location | Call number | Status | Date due | Barcode | Item holds |
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Book | Chennai Mathematical Institute General Stacks | 512.44 HEI (Browse shelf) | Available | 11067 |

Formerly CIP. Uk

Includes bibliographical references (pages 407-415) and index.

Tools -- More tools -- First examples of the construction -- The inclusion construction -- Flatness and the Noetherian property -- The flat locus of an extension of polynomial rings -- Excellent rings and formal fibers -- Height-one prime ideals and weak flatness -- Insider Construction details -- Integral closure under extension to the completion -- Iterative examples -- Approximating discrete valuation rings by regular local rings -- Non-Noetherian examples of dimension 3 -- Noetherian properties of non-Noetherian rings -- Non-Noetherian examples in higher dimension -- The Homomorphic Image Construction -- Catenary local rings with geometrically normal formal fibers -- An Ogoma-like examples -- Multi-ideal-adic completions of Noetherian rings -- Noetherian flatness and multi-adic constructions -- Idealwise algebraic independence -- Idealwise algebraic independence II -- Krull domains with Noetherian x-adic completions -- Inclusion Constructions over excellent normal local domains -- Weierstrass techniques for generic fiber rings -- Generic fiber rings of mixed polynomial-power series rings -- Mixed polynomial-power series rings and relations among their spectra -- Extensions of local domains with trivial generic fiber -- Constructions and examples discussed in this book.

Also issued online.