Around Podewski's conjecture

Krzysztof Krupiński, Predrag Tanović, and Frank O. Wagner. "Around Podewski's conjecture." Fundamenta Mathematicae 222.2 (2013): 175-193. <http://eudml.org/doc/283137>.

@article{KrzysztofKrupiński2013,
abstract = { A long-standing conjecture of Podewski states that every minimal field is algebraically closed. Known in positive characteristic, it remains wide open in characteristic zero. We reduce Podewski's conjecture to the (partially) ordered case, and we conjecture that such fields do not exist. We prove the conjecture in case the incomparability relation is transitive (the almost linear case). We also study minimal groups with a (partial) order, and give a complete classification of almost linear minimal groups as certain valued groups. },
author = {Krzysztof Krupiński, Predrag Tanović, Frank O. Wagner},
journal = {Fundamenta Mathematicae},
keywords = {Podewski's conjecture; minimal field; minimal group; valued group},
language = {eng},
number = {2},
pages = {175-193},
title = {Around Podewski's conjecture},
url = {http://eudml.org/doc/283137},
volume = {222},
year = {2013},
}

TY - JOUR
AU - Krzysztof Krupiński
AU - Predrag Tanović
AU - Frank O. Wagner
TI - Around Podewski's conjecture
JO - Fundamenta Mathematicae
PY - 2013
VL - 222
IS - 2
SP - 175
EP - 193
AB - A long-standing conjecture of Podewski states that every minimal field is algebraically closed. Known in positive characteristic, it remains wide open in characteristic zero. We reduce Podewski's conjecture to the (partially) ordered case, and we conjecture that such fields do not exist. We prove the conjecture in case the incomparability relation is transitive (the almost linear case). We also study minimal groups with a (partial) order, and give a complete classification of almost linear minimal groups as certain valued groups.
LA - eng
KW - Podewski's conjecture; minimal field; minimal group; valued group
UR - http://eudml.org/doc/283137
ER -