Around Podewski%26apos;s conjecture

作者：Krupinski Krzysztof^*; Tanovic Predrag; Wagner Frank O

来源：Fundamenta Mathematicae, 2013, 222(2): 175-193.

DOI：10.4064/fm222-2-4

• Podewski%26apos
• s conjecture
• minimal field
• minimal group
• valued group

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%26apos;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). %26lt;br%26gt;We also study minimal groups with a (partial) order, and give a complete classification of almost linear minimal groups as certain valued groups.

• 出版日期2013