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Construction of an epimorphism of projective planes over Cartesian groups. (English) Zbl 0698.51001

If \((L,+,e,\leq)\) is an ordered loop and T is a Cartesian field with commutative addition, then the set D of all maps f: \(L\to T\) with well- ordered support, taken with pointwise addition and the product \((f\cdot g)(z)=\sum_{x+y=z}f(x)g(y)\) is again a Cartesian field. Put \(\phi (f)=f(e)\) if \(f(x)=0\) for all \(x<e\) and \(\phi (f)=\infty\) otherwise. The author shows that \(\phi\) : \(D\to T\cup \{\infty \}\) is a place.
Reviewer: H.Salzmann

MSC:

51A10 Homomorphism, automorphism and dualities in linear incidence geometry
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References:

[1] Vanžurová A.: Homomorphisms of projective planes over quasifields and nearfields. Acta Univ. Palac. Olomucensis, fac.rer.nat. 69 (1981), 35-40. · Zbl 0504.51005
[2] Vanžurová A.: Places of alternative fields. AUPO 69 (1981), 41-46. · Zbl 0481.17007
[3] Vanžurová A.: On generalized formal power series. AUPO, to appear. · Zbl 0635.16001
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