000 | 03035nam a22004575i 4500 | ||
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001 | 978-3-319-03212-2 | ||
003 | DE-He213 | ||
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007 | cr nn 008mamaa | ||
008 | 140320s2014 gw | s |||| 0|eng d | ||
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_a10.1007/978-3-319-03212-2 _2doi |
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_a512.44 _223 |
100 | 1 |
_aKnebusch, Manfred. _eauthor. _4aut _4http://id.loc.gov/vocabulary/relators/aut |
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245 | 1 | 0 |
_aManis Valuations and Prüfer Extensions II _h[electronic resource] / _cby Manfred Knebusch, Tobias Kaiser. |
264 | 1 |
_aCham : _bSpringer International Publishing : _bImprint: Springer, _c2014. |
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300 |
_aXII, 190 p. _bonline resource. |
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336 |
_atext _btxt _2rdacontent |
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337 |
_acomputer _bc _2rdamedia |
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338 |
_aonline resource _bcr _2rdacarrier |
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347 |
_atext file _bPDF _2rda |
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490 | 1 |
_aLecture Notes in Mathematics, _x0075-8434 ; _v2103 |
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505 | 0 | _aOverrings and PM-Spectra -- Approximation Theorems -- Kronecker extensions and star operations -- Basics on Manis valuations and Prufer extensions -- Multiplicative ideal theory -- PM-valuations and valuations of weaker type -- Overrings and PM-Spectra -- Approximation Theorems -- Kronecker extensions and star operations -- Appendix -- References -- Index. | |
520 | _aThis volume is a sequel to “Manis Valuation and Prüfer Extensions I,” LNM1791. The Prüfer extensions of a commutative ring A are roughly those commutative ring extensions R / A,where commutative algebra is governed by Manis valuations on R with integral values on A. These valuations then turn out to belong to the particularly amenable subclass of PM (=Prüfer-Manis) valuations. While in Volume I Prüfer extensions in general and individual PM valuations were studied, now the focus is on families of PM valuations. One highlight is the presentation of a very general and deep approximation theorem for PM valuations, going back to Joachim Gräter’s work in 1980, a far-reaching extension of the classical weak approximation theorem in arithmetic. Another highlight is a theory of so called “Kronecker extensions,” where PM valuations are put to use in arbitrary commutative ring extensions in a way that ultimately goes back to the work of Leopold Kronecker. | ||
650 | 0 | _aAlgebra. | |
650 | 1 | 4 |
_aCommutative Rings and Algebras. _0http://scigraph.springernature.com/things/product-market-codes/M11043 |
700 | 1 |
_aKaiser, Tobias. _eauthor. _4aut _4http://id.loc.gov/vocabulary/relators/aut |
|
710 | 2 | _aSpringerLink (Online service) | |
773 | 0 | _tSpringer eBooks | |
776 | 0 | 8 |
_iPrinted edition: _z9783319032115 |
776 | 0 | 8 |
_iPrinted edition: _z9783319032139 |
830 | 0 |
_aLecture Notes in Mathematics, _x0075-8434 ; _v2103 |
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856 | 4 | 0 | _uhttps://doi.org/10.1007/978-3-319-03212-2 |
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