Subfields of a real closed field of countable codimension

[摘要] Given a real closed field R we provide an elementary method to construct directed systems {K-n: n is an element of N} of subfields of Rof countable codimension, that is, the dimension of R as K-n-vector space is N-0, such that R= lim -> K-n. Next we deduce some properties of the family of subfields of countable codimension of a real closed field. (c) 2021 Elsevier B.V. All rights reserved.

[发布日期] 2021-12-01

[关键词] Real closed field;Galois theory;Krull topology