A discrete form of the theorem that each field endomorphism of R (Q_p) is the identity
| dc.creator | Tyszka, Apoloniusz | |
| dc.date | 2003-09-22 | |
| dc.date | 2005-09-13 | |
| dc.date.accessioned | 2026-07-07T06:31:30Z | |
| dc.date.available | 2026-07-07T06:31:30Z | |
| dc.description | Let K be a field and F denote the prime field in K. Let \tilde{K} denote the set of all r \in K for which there exists a finite set A(r) with {r} \subseteq A(r) \subseteq K such that each mapping f:A(r) \to K that satisfies: if 1 \in A(r) then f(1)=1, if a,b \in A(r) and a+b \in A(r) then f(a+b)=f(a)+f(b), if a,b \in A(r) and a \cdot b \in A(r) then f(a \cdot b)=f(a) \cdot f(b), satisfies also f(r)=r. Obviously, each field endomorphism of K is the identity on \tilde{K}. We prove: \tilde{K} is a countable subfield of K, if char(K) \neq 0 then \tilde{K}=F, \tilde{C}=Q, if each element of K is algebraic over F=Q then \tilde{K}={x \in K: x is fixed for all automorphisms of K}, \tilde{R} is equal to the field of real algebraic numbers, \tilde{Q_p}={x \in Q_p: x is algebraic over Q}. | |
| dc.description | to appear in Aequationes Math., Theorem 5 provides a new characterization of \tilde{K} | |
| dc.identifier | https://arxiv.org/abs/math/0309346 | |
| dc.identifier | http://arxiv.org/abs/math/0309346 | |
| dc.identifier | Aequationes Mathematicae 71 (2006), no. 1-2, pp. 100-108 | |
| dc.identifier | doi:10.1007/s00010-005-2801-y | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/98625 | |
| dc.subject | Number Theory | |
| dc.subject | Metric Geometry | |
| dc.subject | 12E99, 12L12 | |
| dc.title | A discrete form of the theorem that each field endomorphism of R (Q_p) is the identity | |
| dc.type | text |