naa a22 4500 510783155 CHVBK 20180411083254.0 cr unu---uuuuu 180411e20130801xx s 000 0 eng 10.1007/s11856-012-0160-7 doi (NATIONALLICENCE)springer-10.1007/s11856-012-0160-7 Steinitz classes for Galois extensions of Dedekind rings [Elektronische Daten] [Rebecca Roy, Peter Schmid] Galois extensions of commutative rings have been studied by Chase, Harrison, Rosenberg and others. Suppose B|A is such an extension with (finite) group G where both A and B are Dedekind rings. Then the Steinitz class s B|A is an element in the class group Cl(A) which vanishes if and only if B is a free A-module. It is shown that s B|A = 1 except possibly when the characteristic char(A) ≠ 2 and G has a cyclic Sylow 2-subgroup ≠ 1. In the exceptional case there is a unique (normal) subgroup H of G with index 2 and s B|A = s C|A where C = B H is the fixed ring. The remaining quadratic case is known and easily treated. Hebrew University Magnes Press, 2013 Roy Rebecca Mathematisches Institut der Universität Tübingen, Auf der Morgenstelle 10, 72076, Tübingen, Germany aut Schmid Peter Mathematisches Institut der Universität Tübingen, Auf der Morgenstelle 10, 72076, Tübingen, Germany aut Israel Journal of Mathematics Springer US; http://www.springer-ny.com 196/1(2013-08-01), 285-293 0021-2172 196:1<285 2013 196 11856 https://doi.org/10.1007/s11856-012-0160-7 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s11856-012-0160-7 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Roy Rebecca Mathematisches Institut der Universität Tübingen, Auf der Morgenstelle 10, 72076, Tübingen, Germany aut NATIONALLICENCE 700 1- Schmid Peter Mathematisches Institut der Universität Tübingen, Auf der Morgenstelle 10, 72076, Tübingen, Germany aut NATIONALLICENCE 773 0- Israel Journal of Mathematics Springer US; http://www.springer-ny.com 196/1(2013-08-01), 285-293 0021-2172 196:1<285 2013 196 11856 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer