## 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

### Keywords:

epimorphism for projective planes; Cartesian groups
Full Text:

### 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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