Vanžurová, Alena Construction of an epimorphism of projective planes over Cartesian groups. (English) Zbl 0698.51001 Acta Univ. Palacki. Olomuc., Fac. Rerum Nat. 91, Math. 27, 49-53 (1988). 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 PDF BibTeX XML Cite \textit{A. Vanžurová}, Acta Univ. Palacki. Olomuc., Fac. Rerum Nat., Math. 27, 49--53 (1988; Zbl 0698.51001) Full Text: EuDML OpenURL 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 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.