Cargando…

Manis Valuations and Prüfer Extensions II

This 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...

Descripción completa

Detalles Bibliográficos
Clasificación:Libro Electrónico
Autores principales: Knebusch, Manfred (Autor), Kaiser, Tobias (Autor)
Autor Corporativo: SpringerLink (Online service)
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Cham : Springer International Publishing : Imprint: Springer, 2014.
Edición:1st ed. 2014.
Colección:Lecture Notes in Mathematics, 2103
Temas:
Acceso en línea:Texto Completo

MARC

LEADER 00000nam a22000005i 4500
001 978-3-319-03212-2
003 DE-He213
005 20220116192934.0
007 cr nn 008mamaa
008 140320s2014 sz | s |||| 0|eng d
020 |a 9783319032122  |9 978-3-319-03212-2 
024 7 |a 10.1007/978-3-319-03212-2  |2 doi 
050 4 |a QA251.3 
072 7 |a PBF  |2 bicssc 
072 7 |a MAT002010  |2 bisacsh 
072 7 |a PBF  |2 thema 
082 0 4 |a 512.44  |2 23 
100 1 |a Knebusch, Manfred.  |e author.  |4 aut  |4 http://id.loc.gov/vocabulary/relators/aut 
245 1 0 |a Manis Valuations and Prüfer Extensions II  |h [electronic resource] /  |c by Manfred Knebusch, Tobias Kaiser. 
250 |a 1st ed. 2014. 
264 1 |a Cham :  |b Springer International Publishing :  |b Imprint: Springer,  |c 2014. 
300 |a XII, 190 p.  |b online resource. 
336 |a text  |b txt  |2 rdacontent 
337 |a computer  |b c  |2 rdamedia 
338 |a online resource  |b cr  |2 rdacarrier 
347 |a text file  |b PDF  |2 rda 
490 1 |a Lecture Notes in Mathematics,  |x 1617-9692 ;  |v 2103 
505 0 |a Overrings 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 |a This 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 |a Commutative algebra. 
650 0 |a Commutative rings. 
650 1 4 |a Commutative Rings and Algebras. 
700 1 |a Kaiser, Tobias.  |e author.  |4 aut  |4 http://id.loc.gov/vocabulary/relators/aut 
710 2 |a SpringerLink (Online service) 
773 0 |t Springer Nature eBook 
776 0 8 |i Printed edition:  |z 9783319032115 
776 0 8 |i Printed edition:  |z 9783319032139 
830 0 |a Lecture Notes in Mathematics,  |x 1617-9692 ;  |v 2103 
856 4 0 |u https://doi.uam.elogim.com/10.1007/978-3-319-03212-2  |z Texto Completo 
912 |a ZDB-2-SMA 
912 |a ZDB-2-SXMS 
912 |a ZDB-2-LNM 
950 |a Mathematics and Statistics (SpringerNature-11649) 
950 |a Mathematics and Statistics (R0) (SpringerNature-43713)