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Chain geometries over local alternative algebras

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Abstract

In this paper, chain geometries over local alternative algebras are introduced. We determine the isomorphisms between them, and embed them into chain geometries over associative algebras.

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References

  1. Benz, W.:Vorlesungen über Geometrie der Algebren, Springer, Berlin, 1973.

    Google Scholar 

  2. Blunck, A.:Doppelverhältnisse und lokale Alternativringe, Dissertation, Universität Hamburg, 1990.

  3. Blunck, A.: Cross-ratios over local alternative rings,Results Math. 19 (1991), 246–256.

    Google Scholar 

  4. Blunck, A.: Projectivities in Moufang-Klingenberg planes,Geom. Dedicata 40 (1991), 341–359.

    Google Scholar 

  5. Blunck, A.: Cross-ratios in Moufang-Klingenberg planes, to appear inGeom. Dedicata.

  6. Herzer, A.: On isomorphisms of chain geometries,Note di Mat. 8 (1987), 251–270.

    Google Scholar 

  7. Herzer, A.: Chain Geometries, in:Handbook of Incidence Geometry, ed. F. Buekenhout, North-Holland, Amsterdam, to appear.

  8. Jacobson, N.:Structure and Representations of Jordan Algebras, AMS Coll. Publ.39, Providence, 1968.

  9. Kroll, H.-J.: Unterräume von Kettengeometrien und Kettengeometrien mit Quadrikenmodell,Results Math. 19 (1991) 327–334.

    Google Scholar 

  10. Limaye, B.V., Limaye, N.B.: The fundamental theorem for the projective line over non-commutative local rings,Arch. Math. 28 (1977), 102–109.

    Google Scholar 

  11. Mäurer, H., Metz, R., Nolte, W.: Die Automorphismengruppe der Möbiusgeometrie einer Körpererweiterung,Aequationes Math. 21 (1980), 110–112.

    Google Scholar 

  12. Schaeffer, H.: Zur Möbiusgeometrie über Alternativkörpern,Geom. Dedicata 10 (1981), 183–189.

    Google Scholar 

  13. Zhevlakov, K.A., Slin'ko, A.M., Shestakov, I.P., Shirshov, A.L.:Rings That Are Nearly Associative, Academic Press, New York, 1982.

    Google Scholar 

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Dedicated to Professor Rafael Artzy on the occasion of his 80th birthday

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Blunck, A. Chain geometries over local alternative algebras. J Geom 44, 33–44 (1992). https://doi.org/10.1007/BF01228280

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  • DOI: https://doi.org/10.1007/BF01228280

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