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- W2899932738 abstract "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}." @default.
- W2899932738 created "2018-11-16" @default.
- W2899932738 creator A5082814024 @default.
- W2899932738 date "2004-01-21" @default.
- W2899932738 modified "2023-09-24" @default.
- W2899932738 title "A new countable subfield tilde{K} of any field K such that each field endomorphism of K is the identity on tilde{K}" @default.
- W2899932738 hasPublicationYear "2004" @default.
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