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Desargues theorem for Klingenberg projective plane over certain local ring. (English) Zbl 0961.51002

Let \(PK(2,R)\) be the projective Klingenberg plane obtained from the free left module \(M_R\) of rank three over a local ring \(R\).
The author proves that an analogue for the configurational theorem of Desargues valid in the ordinary projective plane \(PG(2,K)\) over a skewfield \(K\), holds in \(PK(2,R)\).

MSC:

51C05 Ring geometry (Hjelmslev, Barbilian, etc.)
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References:

[1] Anderson F. W., Fuller F. K.: Rings and Categories of Modules. Springer-Verlag, New York, 1973.
[2] Atiyah M. F., MacDonald I. G.: Introduction to commutative algebra. Mir, Moskva, 1972 · Zbl 0238.13001
[3] Jukl M.: Grassmann formula for certain type of modules. Acta Univ. Palacki. Olomuc., Fac. rer. nat., Math. 34 (1995), 69-74. · Zbl 0860.13006
[4] Klingenberg W.: Projektive Geometrien mit Homomorphismus. Math. Annalen 132 (1956), 180-200. · Zbl 0073.36404
[5] Machala F.: Fundamentalsatze der projektiven Geometrie mit Homomorphismus. Rozpravy ČSAV, řada mat. a přír. v\?d, 90, sešit 5, Praha, Academia, 1980. · Zbl 0457.51003
[6] Machala F.: Desarguessche Affine Ebenen mit Homomorphismus. Geometriae Dedicata 3 (1975), 493-509. · Zbl 0302.50002
[7] McDonald B. R.: Geometric algebra over local rings. Pure and applied mathematics, New York, 1976. · Zbl 0346.20027
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