n-th root selections in fields



Abstract

In this work we generalize the results of [9] to the higher level case: we define n-th root selections in fields of characteristic ≠2, that is subgroups of the multiplicative group of a field whose existence is equivalent to the existence of a partial inverse of the xxn function, provide necessary and sufficient conditions for such a subgroup to exist, study their existence under field extensions, and give some structural results describing the behaviour of maximal n-th root selection fields.


Keywords

root selections; root selections of higher level; half-orderings; pre-orderings and orderings of higher level

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Published : 2019-06-22


GładkiP. (2019). n-th root selections in fields. Annales Mathematicae Silesianae, 33, 106-120. Retrieved from https://journals.us.edu.pl/index.php/AMSIL/article/view/13655

Paweł Gładki  pawel.gladki@us.edu.pl
Instytut Matematyki, Uniwersytet Śląski w Katowicach  Poland



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