LATTICE-ISOMORPHIC GROUPS, AND INFINITE ABELIAN <i>G</i>-COGALOIS FIELD EXTENSIONS
| dc.contributor.author | Albu, Toma | |
| dc.contributor.author | Basarab, Serban | |
| dc.date.accessioned | 2024-07-05T15:09:02Z | |
| dc.date.available | 2024-07-05T15:09:02Z | |
| dc.date.issued | 2002 | |
| dc.department | Atılım University | en_US |
| dc.department-temp | [Albu, Toma] Atilim Univ, Dept Math, TR-06836 Ankara, Turkey; [Basarab, Serban] Romanian Acad, Inst Math Simion Stoilow, RO-70700 Bucharest 1, Romania | en_US |
| dc.description.abstract | The aim of this paper is to provide a proof of the following result claimed by Albu (Infinite field extensions with Galois-Cogalois correspondence (II), Revue Roumaine Math. Pures Appl. 47 (2002), to appear): The Kneser group Kne(E/F) of an Abelian G-Cogalois extension E/F and the group of continuous characters Ch(Gal(E/F)) of its Galois group Gal(E/F) are isomorphic (in a noncanonical way). The proof we give in this paper explains why such an isomorphism is expected, being based on a classical result of Baer (Amer. J. Math. 61 (1939), 1-44) devoted to the existence of group isomorphisms arising from lattice isomorphisms of their lattices of subgroups. | en_US |
| dc.description.sponsorship | Alexander von Humboldt Foundation; Consiliul National al Cercetarii Stiintifice din Invatamantul Superior, Romania; grant of Romanian Academy | en_US |
| dc.description.sponsorship | This work was completed during the stay of the first author at the Heinrich-Heine University of Dusseldorf as a Humboldt Fellow in April-June 2001. He is very indebted to the University for hospitality and to the Alexander von Humboldt Foundation for financial support. He gratefully acknowledges partial support from grant D-7 awarded by the Consiliul National al Cercetarii Stiintifice din Invatamantul Superior, Romania. He would also like to thank Mihai Sabac for helpful discussions on characters of locally compact Abelian groups.r The second author gratefully acknowledges partial support from a grant of the Romanian Academy. | en_US |
| dc.identifier.citation | 3 | |
| dc.identifier.doi | 10.1142/S0219498802000069 | |
| dc.identifier.endpage | 253 | en_US |
| dc.identifier.issn | 0219-4988 | |
| dc.identifier.issn | 1793-6829 | |
| dc.identifier.issue | 3 | en_US |
| dc.identifier.startpage | 243 | en_US |
| dc.identifier.uri | https://doi.org/10.1142/S0219498802000069 | |
| dc.identifier.uri | https://hdl.handle.net/20.500.14411/1136 | |
| dc.identifier.volume | 1 | en_US |
| dc.identifier.wos | WOS:000209819800001 | |
| dc.identifier.wosquality | Q3 | |
| dc.language.iso | en | en_US |
| dc.publisher | World Scientific Publ Co Pte Ltd | en_US |
| dc.relation.publicationcategory | Makale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanı | en_US |
| dc.rights | info:eu-repo/semantics/closedAccess | en_US |
| dc.subject | Lattice-isomorphism of groups | en_US |
| dc.subject | infinite Galois extension | en_US |
| dc.subject | Abelian extension | en_US |
| dc.subject | G-Cogalois extension | en_US |
| dc.subject | G-Kneser extension | en_US |
| dc.subject | locally compact Abelian group | en_US |
| dc.subject | character group | en_US |
| dc.title | LATTICE-ISOMORPHIC GROUPS, AND INFINITE ABELIAN <i>G</i>-COGALOIS FIELD EXTENSIONS | en_US |
| dc.type | Article | en_US |
| dspace.entity.type | Publication |