Spreads of right quadratic skew field extensions | Zendy

Hans Havlicek | Zendy

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Spreads of right quadratic skew field extensions

Author(s) -

Hans Havlicek

Publication year - 1994

Publication title -

geometriae dedicata

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.746

H-Index - 43

eISSN - 1572-9168

pISSN - 0046-5755

DOI - 10.1007/bf01610624

Subject(s) - mathematics , skew , quadratic equation , projective space , projective geometry , pure mathematics , field (mathematics) , isomorphism (crystallography) , projective plane , invariant (physics) , discrete mathematics , combinatorics , differential geometry , geometry , projective test , computer science , crystal structure , chemistry , correlation , crystallography , telecommunications , mathematical physics

LetL/K be a right quadratic (skew) field extension and let be a 3-dimensional projective space overK which is embedded in a 3-dimensional projective space overL. Moreover, let I be a line of which carries no point of. The main result is that — even whenL orK is a skew field — the following holds true: A Desarguesian spread of is given by the set of all lines of which are indicated by the points of I. A spread of arises in this way if, and only if, there exists an isomorphism ofL onto the kernel of the spread such thatK is elementwise invariant. Furthermore, a geometric characterization of right quadratic extensions with a left degree other than 2 and of quadratic Galois extensions is given.

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