Mathematics – Algebraic Geometry
Scientific paper
2006-06-20
Mathematics
Algebraic Geometry
2 pages, 1 table
Scientific paper
A list of different types of a projective line over non-commutative rings with unity of order up to thirty-one inclusive is given. Eight different types of such a line are found. With a single exception, the basic characteristics of the lines are identical to those of their commutative counterparts. The exceptional projective line is that defined over the non-commutative ring of order sixteen that features ten zero-divisors and it most pronouncedly differs from its commutative sibling in the number of shared points by the neighbourhoods of three pairwise distant points (three versus zero), that of "Jacobson" points (zero versus five) and in the maximum number of mutually distant points (five versus three).
Planat Michel
Pracna Petr
Saniga Metod
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