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Projective geometry over an algebra

Published online by Cambridge University Press:  26 February 2010

J. W. Archbold
J. W. Archbold
Affiliation:
University College, London
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Extract

The idea of a geometry in which the coordinates are elements of a linear algebra, instead of the conventional field, goes back to C. Segre. Most of the subsequent work seems to have been done by N. Spampinato who developed some general results and applied them particularly to the case of an algebra of dual numbers defined over the complex field; in general, his aim appears to have been the study of algebraic varieties in the new kind of space.

Type
Research Article
Information
Mathematika , Volume 2 , Issue 2 , December 1955 , pp. 105 - 115
Copyright
Copyright © University College London 1955

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References

page 105 note * Segre, C., “Le geometrie proiettive nei campi di numeri duali”, Atti Torino, 47 (1912), 114–133 and 164–185.Google Scholar

page 105 note † Spampinato, N., “Teoria delle caratteristiche in un' algebra dotata di modulo ed S r, ipercomplessi”, Mem. R. Acc. Lincei, Ser. VI, Vol. VI (1936), 187–259Google Scholar; “Sulla geoiaetria dell' S r biduale proiettivo”, Ibid, VII (1938), 239–296. For later papers, see Mathematical Reviews.

page 114 note * See a paper written in collaboration with N. L. Johnson: “A method of constructing partially balanced incomplete block designs”, to appear in the Annals of Mathematical Statistics.