TY - JOUR
T1 - Functorial equations for lexicographic products
AU - Kuhlmann, Franz Viktor
AU - Kuhlmann, Salma
AU - Shelah, Saharon
PY - 2003/10
Y1 - 2003/10
N2 - We generalize the main result of an earlier paper by the authors (Exponentiation in power series fields, Proc. Amer. Math. Soc. 125 (1997), 3177-3183) concerning the convex embeddings of a chain Γ in a lexicographic power ΔΓ. For a fixed non-empty chain Δ, we derive necessary and sufficient conditions for the existence of non-empty solutions Γ to each of the lexicographic functorial equations (ΔΓ)≤0 ≃ Γ, (Δ Γ)≤0 ≃ Γ and (Δ Γ)≤0 ≃ Γ.
AB - We generalize the main result of an earlier paper by the authors (Exponentiation in power series fields, Proc. Amer. Math. Soc. 125 (1997), 3177-3183) concerning the convex embeddings of a chain Γ in a lexicographic power ΔΓ. For a fixed non-empty chain Δ, we derive necessary and sufficient conditions for the existence of non-empty solutions Γ to each of the lexicographic functorial equations (ΔΓ)≤0 ≃ Γ, (Δ Γ)≤0 ≃ Γ and (Δ Γ)≤0 ≃ Γ.
UR - http://www.scopus.com/inward/record.url?scp=0141907333&partnerID=8YFLogxK
U2 - 10.1090/S0002-9939-03-06830-8
DO - 10.1090/S0002-9939-03-06830-8
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AN - SCOPUS:0141907333
SN - 0002-9939
VL - 131
SP - 2969
EP - 2976
JO - Proceedings of the American Mathematical Society
JF - Proceedings of the American Mathematical Society
IS - 10
ER -