Geodesic
Ring geometries and their lattices
Fundamentalʹnaâ i prikladnaâ matematika, Tome 11 (2005) no. 3, pp. 127-137.

Voir la notice de l'article provenant de la source Math-Net.Ru

We construct a notion of a generalized geometrical lattice, allowing us to obtain an analog of matroid theory for the case of arbitrary principal ideal rings. 
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A. A. Lashkhi. Ring geometries and their lattices. Fundamentalʹnaâ i prikladnaâ matematika, Tome 11 (2005) no. 3, pp. 127-137. http://geodesic.mathdoc.fr/item/FPM_2005_11_3_a8/

[1] Lashkhi A. A., “Aksiomatika P1-proektivnoi geometrii”, Soobsch. AN Gruzinskoi SSR, 130:1 (1988), 37–40 | MR | Zbl

[2] Barbilian D., “Zur Axiomatik der projektiven ebenen Ringgeometrien, I, II”, Jber. Deutsch. Math.-Verein., 50 (1940), 179–229 ; 51 (1941), 34–76 | MR | Zbl | MR | Zbl

[3] Bartolone C., Bartolozzi F., “Topics in geometric algebra over rings”, Rings and Geometry (Istanbul, 1984), NATO Adv. Sci. Inst. Ser. C. Math. Phys. Sci., 160, Reidel, Dordrecht, 1985, 353–389 | MR

[4] Birkhoff G., Lattice Theory, AMS, Providence, 1967 | MR | Zbl

[5] Brehm U., “Coordinatization of lattices”, Rings and Geometry (Istanbul, 1984), NATO Adv. Sci. Inst. Ser. C. Math. Phys. Sci., 160, Reidel, Dordrecht, 1985, 511–550 | MR

[6] Brehm U., Greferath M., Schmidt S. E., “Projective geometry on modular lattices”, Handbook of Incidence Geometry, North-Holland, Amsterdam, 1995, 1115–1142 | MR | Zbl

[7] Grätzer G., General Lattice Theory, Academic Press, New York, 1978 | MR | Zbl

[8] F. Buekenhout (ed.), Handbook of Incidence Geometry. Buildings and Foundations, North-Holland, Amsterdam, 1995 | MR

[9] Lashkhi A. A., “General geometric lattices and projective geometry of modules”, J. Math. Sci., 74:3 (1995), 1044–1077 | DOI | MR | Zbl

[10] Maeda F., Maeda S., Theory of Symmetric Lattices, Springer, New York, 1970 | MR | Zbl

[11] McDonald B. R., Linear Algebra over Commutative Rings, Marcel Dekker, New York, 1984 | MR | Zbl

[12] Neumann J., Continuous Geometry, Princeton Univ. Press, 1960 | MR | Zbl